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ELECTRIC  ARCS 

EXPERIMENTS     UPON     ARCS    BETWEEN 

DIFFERENT  ELECTRODES  IN  VARIOUS 

ENVIRONMENTS    AND    THEIR 

EXPLANATION 


BY 

CLEMENT  D.  CHILD,  PH.  D, 

PROFESSOR  OF  PHYSICS  AT  COLGATE  UNIVERSITY 


58  ILLUSTRATIONS 


NEW  YORK 

D.  VAN  NOSTRAND  COMPANY 

25  PARK  PLACE 
1913 


o 


Engineering 
Library 


COPYRIGHT,  1913, 

BY 
D.  VAN  NOSTRAND  COMPANY 


Stanbope  iprcss 

T.    H.GILSON   COMPANY 
BOSTON,  U.S.A. 


PREFACE. 


WHILE  the  electric  arc  is  one  of  the  most  common  things 
of  modern  life,  an  understanding  of  it  is  not  common. 
This  is  largely  due  to  the  difficulty  of  becoming  familiar 
with  the  investigations  which  have  been  made  on  this 
subject.  There  have  indeed  been  many  articles  published 
concerning  it,  but  they  are  scattered  through  many  pub- 
lications, and  the  data  given  by  different  experimenters  are 
not  consistent  with  each  other,  and  none  of  the  explanations 
are  entirely  satisfactory. 

"The  Electric  Arc,"  by  Mrs.  Hertha  Ayrton,  gave  an 
account  of  the  experiments  which  were  performed  prior  to 
1898,  but  very  little  investigation  had  been  made  at  that 
time  of  any  arc  except  the  open  carbon  arc,  and  none  of 
the  explanations  based  on  the  ionic  theory  had  been  given, 
so  that  by  far  the  greater  part  of  what  is  now  known 
concerning  the  arc  could  not  then  be  described.  An  excel- 
lent work  in  German,  "Der  elektrische  Lichtbogen"  by 
Berthold  Monash,  has  more  recently  appeared,  but  this 
deals  but  briefly  with  the  theoretical  side  and  does  not 
meet  the  requirements  of  those  who  would  read  English 
rather  than  German. 

It,  therefore,  seemed  desirable  to  offer  another  dis- 
cussion of  the  electric  arc,  giving  especial  attention  to  the 
explanation  of  the  phenomena  and  to  those  investigations 
which  have  been  made  since  the  publication  of  Mrs. 

iii 

267707 


IV  PREFACE 

Ayrton's  book.  A  rather  full  account  has,  accordingly, 
been  given  to  such  experiments  as  those  on  the  mercury 
arc,  and  to  a  discussion  of  the  more  recent  theories. 

The  use  of  the  arc  in  commercial  ways  has  already  been 
ably  discussed  in  such  books  as  those  on  Electric  Lighting, 
Photometry  and  Wireless  Telephony.  Accordingly,  these 
topics  have  received  less  attention  here. 

A  few  pages,  'however,  are  given  to  photometry  and  to 
the  whistling  arc,  since  these  are  of  interest  from  a  scien- 
tific as  well  as  from  an  industrial  standpoint.  No  account 
has  been  given  concerning  the  use  of  the  arc  in  chemical 
and  metallurgical  processes,  since  its  function  there  ap- 
pears to  be  merely  to  produce  a  high  temperature  and  a 
study  of  these  phenomena  would  give  us  no  knowledge 
concerning  the  arc  itself. 

I  have  endeavored  to  keep  in  mind  the  needs  of  those 
who  may  wish  to  make  investigations  in  the  future.  An 
effort  has,  therefore,  been  made  to  give  references  to  all  the 
important  articles  on  this  subject,  excepting  those  which 
relate  only  to  the  commercial  side  or  to  those  concerning 
investigations  in  which  the  arc  was  merely  a  means  for 
studying  some  other  phenomenon,  as  when  used  to  pro- 
duce the  spectrum  of  a  metal. 

It  would  often  have  made  much  simpler  and  more  satis- 
factory reading,  if  I  could  have  given  a  brief  and  definite 
statement  of  the  laws  governing  the  action  of  the  arc,  in- 
stead of  producing  so  extended  a  review  of  what  different 
experimenters  have  thought  about  these  laws,  but  in  the 
majority  of  cases  it  is  not  yet  known  what  the  laws  are 
and  the  only  available  method  is  to  discuss  the  results  of 
those  who  have  endeavored  to  find  them.  Not  only  is 
there  this  uncertainty  concerning  the  laws,  but  the  expla- 


PREFACE 

nations  often  raise  more  questions  than  they  settle.  This, 
however,  is  not  an  unusual  condition  and  the  explanations 
may,  at  least,  serve  in  helping  others  to  make  complete 
that  which  is  lacking. 

CLEMENT  D.  CHILD. 

HAMILTON,  N.Y. 
Oct.,  1912. 


TABLE  OF  CONTENTS. 


CHAPTER  PAGE 

I.    INTRODUCTION i 

Definition  of  Electric  Arc i 

Appearance  of  Arc 3 

Discovery  of  Arc 5 

II.    ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES 8 

Relation  Between  Potential  Difference,  Current  and  Length 

of  Arc 9 

E.M.F.  Required  as  Distinct  from  Voltage  of  Arc 16 

Hissing  Arc 21 

Fall  of  Potential  in  Different  Parts  of  Arc 22 

Counter  E.M.F.  of  Arc 25 

Meaning  of  "Resistance  of  Arc" 28 

"Negative  Resistance" 31 

"Forward  E.M.F." 33 

Residual  E.M.F 35 

Temperature  of  Arc 40 

Variation  in  the  Temperature  of  the  Arc 44 

Effect  Produced  by  Cooling  Electrodes '. 46 

Size  of  Anode  Crater 48 

Enclosed  Arc 49 

Miscellaneous 50 

III.  ARC  IN  AIR  BETWEEN  OTHER  SUBSTANCES  THAN  CARBON.  . .  53 

Flaming  Arc 54 

Arc  Between  Metals 61 

Arc  Between  Oxides 67 

Magnetite  Arc 67 

Arc  Between  Electrolytes 69 

Arc  Between  Unlike  Electrodes 69 

IV.  ARC  WITH  PRESSURES  GREATER  OR  LESS  THAN  ATMOSPHERIC 

PRESSURE  AND  IN  OTHER  GASES  THAN  AIR 73 

Arc  with  Pressures  Greater  than  One  Atmosphere 73 

Arc  with  Pressures  Less  than  One  Atmosphere 74 

Carbon  Arc  in  a  Vacuum 75 

Metal  Arc  in  a  Vacuum 81 

Arc  in  Other  Gases  than  Air 83 

vii 


viil  TABLE  OF  CONTENTS 

CHAPTER  PAGE 

V.    MERCURY  ARC 87 

Temperature 91 

Characteristic  Curves 93 

Cathode  Drop 96 

Anode  Drop 97 

Electric  Force  Through  Arc 97 

Arc  in  Quartz  Tubes 100 

Velocity  of  Ions 101 

Modification  of  Arc  to  Produce  White  Light 102 

VI.    ALTERNATING  CURRENT  ARC 105 

Between  Carbons 105 

Characteristic  Curves 106 

Current  and  Potential  Difference  at  Different  Phases 107 

"Dynamical"  Characteristic  Curves no 

Fall  of  Potential  in  A.C.  Arc 112 

Phase  Difference  in  Arc 113 

Arc  Between  Metals 114 

Arc  Between  Unlike  Electrodes 118 

Arc  in  Other  Gases  than  Air 119 

Mercury  Arc  Rectifier 120 

VII.    PHOTOMETRY  OF  THE  ELECTRIC  ARC 126 

Distribution  of  Light 128 

Effect  on  Candle  Power  of  Length  of  Arc,  Current,  Etc. .  . .  130 

Intrinsic  Brightness  of  Crater 132 

Flaming  Arcs 132 

Metal,  Including  Mercury,  Arcs 134 

Alternating-current  Arcs 135 

Comparison  of  Different  Kinds  of  Arcs 139 

Spectrum  of  Arc 142 

VIII.    USE  OF  ARC  IN  WIRELESS  TELEPHONY 146 

Whispering  Arc 146 

Whistling  Arc 148 

Application  of  Whistling  Arc  to  Wireless  Telephony 153 

IX.    THEORY  OF  THE  ELECTRIC  ARC 156 

Definition  of  Ions  and  Electrons 156 

Causes  Producing  Ions 158 

lonization  by  Impact 158 

lonization  by  Hot  Solids 159 

Fall  of  Potential  Through  Arc 160 

lonization  at  Surface  of  Cathode  with  Discharge  at  low 

Pressure 161 

lonization  at  Surface  of  Anode > .  162 


TABLE   OF   CONTENTS  ix 

CHAPTER  PAGE 

IX.        lonization  at  Cathode  of  Arc 162 

Assumption  that  Electrons  come  from  Within  the  Cathode.  163 

Second  Explanation  of  lonization  at  Cathode 165 

Cause  which  Determines  the  Amount  of  the  Cathode  Drop.  166 

lonization  at  Anode 168 

Discharge  of  Ions  to  Electrodes 170 

lonization  of  Gas  Between  Electrodes 171 

Velocity  of  the  Ions 176 

Action  of  Arc  not  the  Same  as  in  an  Electrolyte 179 

Variations  in  the  Cathode  Drop 180 

Variations  in  the  Anode  Drop 183 

Variations  in  the  Electric  Force  Through  Arc 184 

Effect  Produced  by  Heating  the  Cathode 185 


THE  ELECTRIC  ARC 


CHAPTER  I. 
INTRODUCTION. 

WE  may  well  speak  of  our  age  as  an  Age  of  Artificial 
Light.  Where  formerly  men  were  obliged  to  exist  with 
only  pine  knots  and  candles  to  lighten  their  paths,  we  are 
now  not  only  flooded  with  light  but  better  and  cheaper 
sources  are  being  continually  devised.  The  illuminating 
engineer  counts  that  year  lost  which  does  not  see  some 
marked  advance  in  the  art  of  producing  light.  Among 
all  the  contestants  for  popular  favor  there  is  one  source  of 
light  which  stands  as  undisputed  king.  Other  lights  may 
answer  the  need  of  the  worker  at  the  desk,  but  when  one 
wants  light  of  the  most  brilliant  sort,  one  turns  to  the 
electric  arc. 

Definition  of  Electric  Arc.  —  An  account  of  the  electric 
arc  might  well  begin  with  a  statement  concerning  the  time 
and  place  when  man's  eye  was  first  dazzled  by  this  phe- 
nomenon, but  unfortunately  we  do  not  know  when  nor 
where  this  occurred.  This  is  not  because  it  took  place  so 
far  back  in  the  beginning  of  things,  but  because  the  earlier 
experimenters  made  no  distinction  between  the  arc  and 
the  spark. 

They  were,  however,  excusable  in  confusing  these 
terms,  for  there  is  no  logical  and  definite  distinction 


ELECTRIC  ARC 

between  the  momentary  spark  formed  on  opening  a  circuit 
and  the  continuous  discharge  which  is  called  an  arc.  By 
gradually  raising  the  E.M.F.  and  decreasing  the  resistance 
of  a  battery  and  shortening  the  distance  between  the  ter- 
minals it  is  possible  to  pass  continuously  from  a  spark 
which  lasts  but  a  small  fraction  of  a  second  to  an  arc 
which  lasts  indefinitely.  Nor  can  we  say  that  either  the 
potential  difference  or  the  current  of  the  momentary  flash 
is  necessarily  either  greater  or  less  than  that  of  the  arc,  and 
yet  whatever  might  be  the  usage  in  a  perfectly  logical 
language,  the  actual  usage  is  to  make  a  distinction  between 
these  two  phenomena.  About  all  that  can  be  said  is  that 
the  discharge  must  last  quite  a  while  in  order  to  be  called 
an  arc.  "Quite  a  while  "  would  appear  to  be  sufficiently 
indefinite  to  meet  the  needs  of  this  case. 

It  is  much  easier  to  distinguish  between  the  arc  and  the 
continuous  discharge  in  a  vacuum  tube  where  the  current 
is  small  and  the  E.M.F.  large,  such  as  that  shown  in  a 
Geissler  or  Crookes  tube,  which  has  also  been  called  by 
some  a  spark.  The  current  in  this  case  is  much  smaller 
than  with  the  arc,  and  the  potential  difference  is  very 
much  higher.  Moreover  with  the  arc  the  potential  differ- 
ence between  the  cathode,  as  the  negative  terminal  is 
called,  and  the  layer  of  gas  in  its  immediate  neighborhood 
is  small,  while  with  the  glow  discharge  it  is  large.  With 
the  former  it  may  be  as  low  as  5  or  6  volts,  while  with  the 
latter  it  must  be  as  high  as  300  volts. 

Difficulty  is,  however,  experienced  in  making  a  dis- 
tinction between  the  arc  and  the  glow  discharge  in  a 
vacuum  when  the  latter  has  for  the  cathode  a  hot  oxide 
of  certain  metals,  as,  for  example,  calcium  oxide.  In  this 
case  the  drop  in  potential  at  the  cathode  may  be  as  small  as 


INTRODUCTION 

that  with  the  arc  and  the  current  as  large,1  and  the  only 
distinction  between  these  two  forms  of  discharge  is  that  in 
the  arc  the  cathode  is  heated  by  the  current  flowing  through 
the  gas,  while  with  the  hot  calcium  oxide  the  cathode  must 
be  heated  by  some  external  source. 

Though  it  is  not  possible  to  make  a  perfect  distinction 
between  what  is  and  what  is  not  an  arc,  we  shall  not  be  far 
from  the  common  usage,  if  we  define  an  arc  as  consisting 
of  a  continuous  current  of  several  amperes  or  more,  passing 
through  a  gas  and  having  a  cathode  drop  which  is  com- 
paratively small.  The  most  common  form  is  that  between 
carbons  in  air  where  the  cathode  drop  is  in  the  neighbor- 
hood of  9  volts  and  the  current  5  amperes  or  more. 

Appearance  of  Arc.  —  There  are  probably  few  people  in 
civilized  countries  who  have  not  seen  an  electric  arc,  and 
yet  it  would  be  nearly  as  truthful  to  say  that  there  are  few 
who  have  seen  one.  There  are  few  who  have  not  seen  a 
frosted  globe  which  was  intensely  luminous  and  was  said 
to  contain  an  electric  arc,  or  who  have  not  been  blinded 
by  looking  too  closely  at  an  uncovered  arc.  On  the  other 
hand,  there  are  few  who  have  seen  the  difference  between 
the  luminous  gas  and  the  even  more  luminous  terminals, 
who  have  seen  the  different  shades  of  this  gas  as  it  varies 
from  the  violet  of  the  brilliant  center  to  the  yellow  of  the 
faintly  luminous  edge,  or  have  seen  the  fiery  particles 
sent  off  from  the  white  hot  carbons,  but  without  seeing 
these  things  one  does  not  in  reality  see  the  electric  arc. 

As  far  as  it  is  possible  to  reproduce  such  a  view  by 
means  of  an  uncolored  photograph,  it  is  done  in  the 
accompanying  illustration,  which  shows  an  arc  be- 
tween carbon  terminals.  Unfortunately  this  does  not  give 
1  Phys.  Rev.,  29,  360;  1909. 


THE  ELECTRIC  ARC 


distinctly  the  boundary 
between  the  carbon  and 
the  luminous  vapor. 
An  outline  drawing  as 
given  in  Fig.  2  may  be 
helpful  for  this  purpose. 
The  carbon  with  the 
depression  at  the  end 
is  the  positive  carbon, 
or  anode,  as  it  is  called, 
while  the  pointed  car- 
bon is  the  negative  end, 
or  cathode.  The  con- 
cave part  of  the  anode, 
marked  c,  is  intensely 
luminous  and  is  called 
the  crater.  With  this 
form  of  arc  by  far  the 
greater  part  of  the  light  comes  from  this  crater.  Since  it  is 
usually  desirable  to  have  the  light  thrown  on 
the  ground  and  not  into  the  sky,  the  anode  is 
placed  above  and  the  cathode  below. 

With  homogeneous  carbons  this  crater  is 
apt  to  form  at  one  side,  with  the  result  that 
much  of  the  light  is  thrown  to  that  side,  while 
the  region  on  the  other  side  is  left  in  com- 
parative darkness.  It  was  found  that  this 
could  be  largely  remedied  by  making  the 
carbons  hollow  and  filling  the  hollow  space 
with  a  softer  quality  of  carbon.  Such  carbons 
are  called  cored  carbons  and  are  commonly  used  for  the 
anode.  Those  which  are  not  cored  are  called  solid  carbons. 


FIG.  i. 


'—-  -C 


FIG.  2. 


INTRODUCTION 

There  is  a  point  on  the  cathode  which  is  also  intensely 
luminous,  but  this  is  much  smaller  than  the  crater,  so  that 
much  less  light  is  received  from  it  than  from  the  anode. 

The  gas  between  the  carbons  is  luminous  and  seen  by 
itself  would  be  considered  brilliantly  so,  but  compared 
with  the  crater  it  gives  but  little  light.  This  at  least  is 
true  of  the  form  of  the  arc  shown  in  the  accompanying 
illustration.  In  the  flaming  arc,  which  is  now  coming  into 
use,  the  vapor  gives  out  more  light  than  the  crater.  In 
that  form  the  distance  between  the  electrodes  is  longer 
and  the  vapor  is  more  luminous  than  in  the  older  form, 
and  the  crater  less  so. 

The  light  from  the  vapor  is  not  due  to  incandescent 
particles,  but  to  the  luminosity  of  the  gas  itself.  This  is 
shown  by  the  fact  that  its  spectrum  is  a  line  spectrum. 
The  different  parts  of  the  vapor  have  different  colors, 
which  will  be  considered  more  in  detail  in  connection  with 
the  spectrum  of  the  arc. 

Discovery  of  the  Arc.  —  As  has  been  stated,  it  is  im- 
possible to  give  the  date  of  the  first  arc,  because  no  at- 
tempt was  made  to  distinguish  between  the  arc  and  the 
spark.  No  mention  was  made  by  the  first  experimenters 
of  the  length  of  time  occupied  by  the  wonderful  flash  they 
described,  and  no  one  measured  the  current.  The  con- 
fusion between  the  two  forms  of  discharge  was  the  more  ex- 
cusable on  their  part,  since  they  were  trying  to  show  that 
the  electricity  from  chemical  action  was  the  same  as  that 
produced  by  friction  and  gave  the  same  kind  of  flash,  but 
it  makes  it  inconvenient  for  one  who  tries  to  write  a  history 
of  this  work.1 

1  The  following  is  a  list  of  a  few  of  the  articles  appearing  in  the  early 
part  of  last  century: 


6  THE  ELECTRIC  ARC 

There  is,  however,  no  question  but  that  it  was  an  arc 
which  Davy  showed  in  his  Bakerian  lecture,  in  1809,  when 
he  described  the  discharge  from  1000  cells  as  a  brilliant 
flame  of  from  one-fourth  inch  to  one-half  inch  in  length. 
The  name,  "  arc,"  appears  to  have  been  given  by  him  in 
1 82 11  because  of  the  bow-shape  of  the  arc  when  occurring 
between  two  horizontal  electrodes. 

Several  experiments  were  made  by  the  early  workers  on 
the  transport  of  material  in  the  arc.2  Some  believed  this 
phenomenon  to  be  akin  to  that  of  electrolysis;  some  be- 
lieved that  what  was  seen  in  the  arc  was  electricity  itself, 
and  though  we  must  reject  this  view,  we  do  it  with  the 
same  feeling  of  sadness  as  that  which  we  experience  when 
we  outgrow  the  fairy  stories  of  our  early  years.  Others 
thought  that  the  light  was  given  off  by  the  hot  particles 
which  are  driven  off  from  the  carbons. 

The  work  of  these  experimenters  is  of  little  importance 

Gilbert,  Gilbert's  Ann.,  7,  161;   1801. 

Pfaflf,  Gilbert's  Ann.,  7,  248  and  516;  1801.     8,  340;  1802. 

Ritter,  Gilbert's  Ann.,  9,  341;   1801. 

Davy,  Journal  of  the  Roy.  Inst.,  I,  166  and  209;   1802. 

Pepys,  The  Monthly  Mag.,  15,  259;   1803. 

Cuthbertson,  Nicholson's  Journal,  8,  97;   1804. 

Daniel,  Phil.  Trans.,  92,  1839. 

Grove,  Phil.  Mag.,  16,  478;   1840. 

De  la  Rive,  C.  R.,  12,  910;  1841. 

Van  Breda,  C.  R.,  23,  262;   1846. 

Despretz,  C.  R.,  28,  757;   1849.     29>  4&  an<i  7°9>   1849. 

Matteucci,  C.  R.,  30,  201;   1850. 

Herwig,  Pogg.  Ann.,  149,  521;   1873. 

Violle,  C.  R.,  117,  33;   1893.      119,  949;   1894. 

Hertzfeld,  Wied.  Ann.,  62,  439;   1897. 

1  Phil.  Trans.,  18,  1821. 

2  Hare,  Sill.  Journ.,  3,  105;    1821. 

Silliman,  Sill.  Journ.,  5,  108;   1822.    6,  342;   1823.     lo,  123;  1825. 


INTRODUCTION 

now,  since  we  know  that  electricity  can  not  be  seen,  that 
the  phenomena  of  the  arc  are  not  the  same  as  those  of 
electrolysis  and  that  the  current  is  not  carried  by  par- 
ticles. That  the  arc  is  not  an  electrolytic  phenomenon  was 
shown  most  conclusively  by  Weedon l  and  will  be  referred 
to  at  a  later  time.  We  may,  therefore,  leave  the  earlier 
work  and  give  our  attention  to  experiments  of  a  somewhat 
later  date. 

1  Paper  presented  at  the  Electro-chemical  Soc.,  at  Washington,  D.  C, 
April,  1904. 


CHAPTER  II. 

ARC  IN  Am  BETWEEN  CARBON  ELECTRODES. 

The  arc  shown  in  Fig.  i  was  one  between  carbon  ter- 
minals. It  is,  however,  possible  to  use  any  solid  which  is 
an  electrical  conductor  or  any  metal  in  the  liquid  state  for 
the  electrodes.  Electrolytes  may  even  be  used,  if  the 
E.M.F.  is  sufficiently  high.  Any  other  gas  or  a  vacuum 
may  take  the  place  of  air.  However,  only  a  few  of  the  dif- 
ferent forms  of  arc  have  been  found  to  be  of  practical  use, 
and  of  these  the  arc  in  air  between  carbon  electrodes  has 
been  the  most  common.  For  the  present  we  may  give  our 
attention  to  this  form  of  arc. 

The  earliest  carbon  electrodes  were  pieces  of  charcoal 
which  had  been  heated  and  plunged  into  mercury  to  make 
them  better  conductors,  but  in  1843  Foucault  found  that 
better  results  were  secured  by  employing  pencils  cut  from 
the  hard  graphitic  carbon  which  is  deposited  on  the  in- 
terior of  gas  retorts.  The  carbon  electrodes  which  are 
used  to-day  are  usually  made  from  retort  or  petroleum 
coke  which  has  but  a  small  percentage  of  ash.  Lampblack 
has  also  been  used  for  this  purpose.  Whichever  is  used, 
it  is  heated  to  a  high  temperature  for  several  hours,  to  drive 
off  any  moisture  or  oil  which  may  adhere  to  it.  This 
heating  increases  the  conductivity  of  the  mass.  It  is 
then  thoroughly  mixed  with  some  such  binder  as  tar,  and 
formed  into  rods  of  the  desired  size  while  under  a  pres- 

8 


ARC   IN  AIR   BETWEEN   CARBON  ELECTRODES  9 

sure  of  1500  to  1800  atmospheres.  These  rods  are  baked 
until  all  volatile  substances  are  driven  off  and  are  then  cut 
into  the,  desired  length. 

If  the  rods  thus  formed  are  homogeneous  they  are  called 
solid  carbons.  Cored  carbons  consist  of  an  outer  cylinder 
which  is  made  by  the.  same  process  as  that  just  described 
and  a  core  which  is  filled  in  after  the  outer  cylinder  is  fin- 
ished. According  to  Mahlke 1  the  core  consists  of  two  parts 
of  baked  lampblack  and  one  part  of  potassium  silicate. 
The  core  usually  has  a  diameter  about  one-fifth  that  of 
the  whole  carbon. 

Relation  Between  Potential  Difference,  Current  and 
Length  of  Arc.  —  One  of  the  first  questions  for  us  to  con- 
sider is  that  concerning  the  amount  of  E.M.F.  necessary 
in  order  to  maintain  the  arc.  The  first  accurate  measure- 
ments taken  for  the  purpose  of  answering  this  question 
were  made  by  Edlund  in  i86y.2  He  found  that  r  =  m  +  nl, 
where  r  is  the  "apparent  resistance/'  that  is  the  ratio 
between  the  voltage  at  the  terminals  of  the  arc  and  the 
current;  /  its  length;  and  m  and  n  quantities  which  are  con- 
stants as  long  as  the  current  is  constant.  He  further  stated 
that  the  voltage  of  the  arc  is  independent  of  the  current, 
and  that  the  "true"  resistance,  represented  by  the  term  nl, 
is  proportional  to  the  length  and  increases  as  the  current 
decreases. 

There  were  at  that  time  no  definite  units  for  measuring 
electrical  quantities  and  no  dynamo  for  producing  the 
current,  so  that  the  accuracy  of  Edlund's  results  seems  to 
have  been  the  result  of  good  fortune  as  well  as  of  careful 

1  Elec.  World.,  57,  672;   1911. 

2  Pogg.  Ann.,  131,  586;  1867.      133,  353;   1868.      134.  250  and  337; 
1868.      139,  354;   1870.      Wied.  Ann.,  26,  518;    1885. 


10  THE  ELECTRIC  ARC 

work.  In  his  explanations  he  was  not  so  fortunate.  His  ex- 
planation was  that  this  "apparent  resistance"  was  partly 
due  to  a  counter  E.M.F.,  which  was  equal  to  the  current 
times  the  m  in  his  formula,  and  partly  to  a  "true"  resist- 
ance corresponding  to  the  term  nl.  The  counter  E.M.F. 
he  found  equivalent  to  23  Bunsen  cells,  which  is  approxi- 
mately 40  volts. 

Though  this  explanation  was  not  fortunate  in  the  sense 
of  being  correct,  it  was  very  fortunate  in  that  it  caused 
much  discussion  on  the  part  of  other  scientists  and  led  to 
many  new  experiments.  These  have  dealt  on  the  one 
hand  with  the  accuracy  of  his  formula,  and  on  the  other 
with  the  truth  of  his  explanation.  It  is  scarcely  of  value 
to  consider  in  detail  the  data  given  by  the  different  ex- 
perimenters. If  we  should  do  so,  we  would  find  that  they 
differ  greatly  among  themselves,  and  the  real  significance 
of  their  work  is  that  there  are  rarely  two  carbons  which 
give  the  same  results.  Even  when  two  carbons  are  ex- 
actly alike  the  data  observed  will  not  be  identical  unless 
the  conditions  are  the  same.1 

For  example,  it  has  been  shown  by  Mrs.  Ayrton2  that 
the  voltage  of  an  arc  when  first  started  is  quite  different 
from  what  it  is  after  it  has  reached  a  steady  condition. 
The  time  required  to  reach  this  state  depends  largely  on 

1  Ayrton  and  Perry,  Proc.  Phys.  Soc.,  5,  197;   1882. 
Cross  and  Shepard,  Proc.  Amer.  Acad.  Sc.,  22,  227;   1886. 
Frolich,  Elektrot.  ZS.,  4,  150;   1883. 

Nebel,  Centralbl.  f.  Elektrot.,  8,  517  and  619;   1886. 
Uppenborn,  Centralbl.  f.  Elektrot.,  9,  633;   1888. 
Luggin,  Centralbl.  f.  Elektrot,  10,  567;   1888. 
Granqvist,  Beib.,  22,  243;   1898. 
Thompson,  Elec.  Rev.,  27,  262;   1895. 

2  Mrs.  Ayrton's  "  Electric  Arc,"  p,  107, 


ARC   IN  AIR   BETWEEN   CARBON   ELECTRODES 


II 


the  shape  which  the  ends  of  the  carbons  have  when  the 
arc  is  started,  but  even  when  their  shape  at  the  beginning 
is  that  which  they  finally  take,  it  is  many  minutes  before 
the  arc  reaches  a  constant  condition. 

The  variation  in  voltage  during  an  hour's  run  is  shown 
in  Fig.  3.     The  current  during  this  time  was  kept  at  10 


20 


20         30         40         50         60 
TIME  IN  MINUTES 


,  3.  _ 

amperes,  and  the  length  of  the  arc  3  mm.  The  negative 
carbon  in  each  case  was  a  solid  carbon  15  mm.  in  diameter. 
This  had  been  shaped  by  being  previously  used  for  a  long 
time  with  an  arc  which  was  also  3  mm.  long  having  a  cur- 
rent of  10  amperes.  In  curve  A  the  positive  carbon  was 
solid  with  the  end  filed  flat  before  the  arc  was  started. 
In  B  the  positive  carbon  was  cored  with  the  end  filed 
flat.  In  C  the  positive  carbon  was  cored  with  a  crater 
mechanically  formed  before  the  arc  was  started.  With 
these  carbons  the  arc  had  hardly  reached  a  constant  con- 
dition at  the  end  of  an  hour. 


12 


THE  ELECTRIC  ARC 


Even  when  the  arc  has  reached  a  constant  cpndition 
with  a  given  current  it  requires  several  minutes  for  it  to 
become  steady  again  if  the  current  is  changed.  This  is 
shown  in  the  curves  given  in  Fig.  4.  The  positive  carbon 
was  13  mm.  in  diameter  and  was  cored,  the  negative  n  mm. 
and  solid.  The  length  of  the  arc  in  the  upper  curve  was 
4  mm.  and  in  the  lower  3  mm. 


5An 

ps. 

50 
4.c 

10  i 

^mps. 

" 

& 

'X 

/ 

I 

16  Ar 

ff°  — 

nps. 

T 

n      25 

Amp« 

res 

'^3 

1  ^' 

Af\ 

5 

I 

Cf) 

45 

f° 

n 

pO—  0 

K 

C 

SKXJ 

40 

r 

&* 

0       10       20      30       40      50       60       70      80      90    '100     11 

TIME  IN  MINUTES 
FIG.  4. 

The  most  careful  examination  of  the  relation  between 
current  and  voltage  has  been  made  by  Mrs.  Ayrton,  and 
some  of  her  results  are  shown  in  the  accompanying  figures. 
Fig.  5  shows  a  series  of  curves,  called  "  characteristic" 
curves,  giving  this  relation  for  different  lengths  of  arcs 
with  solid  carbons.  They  show  clearly  the  difference  be- 
tween the  resistance  of  the  arc  and  that  of  a  metal.  With 
a  metal  the  potential  difference  increases  as  the  current 
increases  and  is  directly  proportional  to  it.  Here  the  volt- 
age decreases  when  the  current  increases.  It  seems  at 
first  as  if  the  greater  the  cause  the  less  the  effect,  but  it 
should  be  noticed  that  while  the  voltage  decreases  the 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES         13 

— -— . 

amount  of  energy  used  in  the  arc  increases.  The  greater 
amount  of  heat  thus  produced  causes  the  conductivity  of 
the  gas  between  the  electrodes  to  be  greater,  and  the  con- 
ductivity increases  so  rapidly  that  the  voltage  needed 
actually  becomes  less  with  the  larger  currents.  Further 


10   12   14   16   18   20   22   24   26   28   30 

CURRENT  IN  AMPERES 
FIG.  5. 


consideration  of  this  will  be  given  in  the  chapter  on  the 
theory  of  the  arc. 

After  decreasing  to  nearly  a  constant  value  the  poten- 
tial suddenly  drops,  as  is  indicated  in  the  dotted  lines  in 
the  curve.  At  this  point  the  arc  begins  to  emit  a  loud, 
hissing  sound.  Such  an  arc  is  called  a  hissing  arc.  This 
will  be  more  fully  described  in  a  following  paragraph. 

A  similar  set  of  curves  is  shown  in  Fig.  6,  where  the 
positive  carbon  is  cored  and  the  negative  one  is  solid. 


14  THE   ELECTRIC   ARC 

Mrs.  Ayrton  found  that  with  the  solid  carbons  which 
she  used  the  relation  between  the  potential  difference, 
current  and  length  of  arc  could  be  expressed  by  the  equa- 
tion 

E  =  38.88  +  2.07  /  +  "-66  +  IO-54* , 

where  E  is  the  potential  difference  between  the  terminals 
in  volts,  /  the  current  in  amperes,  and  /  the  length  of  the 


0   2   4   6   8   10  12  14   16  18  20  22  24-  26  28  30   32  34 
CURRENT  IN  AMPERES 

FlG.  6. 

arc  in  millimeters.  For  cored  carbons  the  relation  could 
not  be  expressed  by  a  simple  equation.  She  believed  that 
this  was  due  to  the  change  which  occurs  when  the  crater 
of  the  anode  begins  to  cover  more  than  the  core  of  the 
carbon. 

The  power  used  in  the  arc  is,  of  course,  equal  to  the 
potential  difference  times  the  current,  so  that  the  equation 
for  the  power  used  in  the  arc  with  solid  carbons  according 
to  Mrs.  Ayrton's  data  is 

P  =  (38.88  +  2.07  0  /  +  11.66  +  10.54  /, 


8    10121416182022242628 
LENGTH   IN  MM, 


ARC  IN  AIR  BETWEEN   CARBON  ELECTRODES         15 

where  P  is  the  power  used.  When  this  equation  is  plotted, 
using  power  for  ordinates  and  current  for  abscissae,  we 
have  a  straight  line. 

When  an  arc  is  very  long,  the  equations  given  by  Mrs. 
Ayrton  do  not  hold,  as  has  been  shown  by  Duddell.1  The 
curve  given  by  her  equation 
and  that  found  experimen- 
tally by  Duddell  are  plotted 
in  Fig.  7.  Duddell  also  found 
a  similar  difficulty  when  the  5 
currents  were  less  than  1.5 
amperes,  the  voltage  then 
being  less  than  that  calcu- 
lated from  Mrs.  Ayr  ton's 
equations. 

The  characteristic  curves  for  arcs  between  solid  carbons 
in  air  and  with  currents  as  small  as  0.6  ampere  were 
observed  by  Malcolm  and  Simon.2  They  give  the  equa- 
tion El  =  49  +  60  /,  when  the  length  is  8  mm.,  and 
El  =  31.  5+  51.5  /,  when  it  is  4  mm. 

We  have  here  been  giving  the  relation  between  the  po- 
tential difference  and  current  for  arcs  that  have  been  run- 
ning sufficiently  long  to  have  reached  a  steady  condition. 
This  is  what  one  usually  wishes  to  know.  An  engineer, 
for  example,  wishes  to  know  the  power  needed  by  a  lamp 
under  certain  constant  conditions.  But  there  are  also 
times  when  one  wishes  to  know  something  about  the  rela- 
tion between  potential  difference  and  current  when  they 
are  changing  rapidly.  Such  knowledge,  for  example,  is 
desirable  when  using  arcs  in  wireless  telephony.  Curves 


FlG- 


1  Phil.  Trans.,  203,  A,  338;   1904. 

2  Phys.  ZS.,  8,  471;   1907. 


1 6  THE   ELECTRIC   ARC 

giving  the  relation  for  steady  conditions  have  been  called 
by  Simon1  "  statical"  characteristic  curves;  those  giving 
the  relation  with  changing  conditions  were  called  "  dynam- 
ical" characteristic  curves. 

The  dynamical  curves  are  found  by  comparing  the 
potential  differences  with  the  currents  for  different  phases 
of  an  alternating-current  arc,  or  when  an  alternating  cur- 
rent is  superimposed  on  a  direct  current  which  is  main- 
taining an  arc.  The  discussion  of  such  curves  will,  there- 
fore, be  considered  in  connection  with  alternating-current 
arcs. 

E.M.F.  Required  as  Distinct  from  Voltage  of  Arc.  —  Arc 
lights  are  commonly  maintained  by  constant  current 
dynamos.  Under  such  conditions  there  is  no  need  of  put- 
ting resistance  in  series  with  the  arc  in  order  to  insure  its 
stability.  But  occasionally  an  arc  is  connected  to  some 
source  maintaining  a  constant  E.M.F.,  as,  for  example,  a 
constant  potential  dynamo.  When  this  is  done,  it  is  neces- 
sary to  put  resistance  in  series  with  the  arc,  as  was  pointed 
out  by  Blondel.2  The  curves  which  have  been  given  show 
the  potential  difference  between  the  electrodes  for  different 
currents,  but  they  do  not  show  the  required  E.M.F.  of  a 
source  having  a  constant  voltage.  Such  E.M.F.  can  be 
found  as  follows : 

Let  us  assume  that  the  potential  difference  is  E  when 
the  current  is  /  for  any  given  length  /.  If  now  the  dynamo 
gave  exactly  E  volts,  and  there  was  no  resistance  in  the 
circuit,  the  system  would  be  in  a  condition  of  unstable 
equilibrium.  For  if  there  were  any  fluctuations  either 
in  the  dynamo  or  in  the  arc  which  gave  a  momentary 

1  Phys.  SZ.,  6,  302;   1905. 

2  Lum.  Elec.,  42,  621;   1891. 


ARC  IN  AIR  BETWEEN   CARBON  ELECTRODES         17 


increase  in  the  current,  the  potential  difference  needed 
for  the  arc  would  be  less  than  the  E.M.F.  of  the  dynamo, 
and  under  such  conditions  the  current  would  increase 
still  further.  This  would  cause  a  further  decrease  in  the 
voltage  used  by  the  arc  and  if  the  E.M.F.  were  main- 
tained, this  process  would  continue  until  the  dynamo  was 
burnt  out. 


-B 


CURRENT 
FIG.    8. 

If  the  current  momentarily  decreased,  a  higher  potential 
difference  would  be  needed  than  the  dynamo  was  giving, 
and  the  arc  would  be  extinguished. 

On  the  other  hand  if  there  is  to  be  resistance  in  the  cir- 
cuit, then  the  E.M.F.  of  the  dynamo  must  be  greater  than 
the  voltage  of  the  arc.  In  order  to  determine  how  much 
greater  the  E.M.F.  must  be,  we  need  to  remember  that 
there  must  be  enough  resistance  in  series  with  the  arc,  so 
that  any  increase  in  the  current  will  produce  a  greater  in- 
crease in  the  drop  in  potential  through  the  resistance 
than  the  decrease  in  voltage  occurring  in  the  arc.  This 
can  perhaps  be  made  clearer  by  referring  to  Fig.  8.  Let 
the  curve  PP'P"  represent  the  relation  between  the  cur- 


1 8  THE   ELECTRIC  ARC 

rent  flowing  through  the  arc  and  the  potential  difference 
at  its  terminal.  The  ordinates  represent  the  voltage  and 
the  abscissae  the  current.  E'  is  the  E.M.F  of  the  dynamo. 
This  is  partly  used  in  maintaining  the  potential  difference 
at  the  terminals  of  the  arc  and  partly  in  maintaining  the 
drop  through  the  resistance.  This  latter  we  will  call  E" . 
As  long  as  this  resistance  is  constant,  E"  will  be  directly 
proportional  to  /,  the  current  flowing  through  the  arc. 
The  vertical  distance  from  the  line  AB  to  any  point  on  the 
straight  line  AP  represents  the  drop  through  this  resistance, 
while  the  abscissa  of  the  point  represents  the  correspond- 
ing current. 

It  is  conceivable  that  with  any  given  resistance  there 
should  be  two  different  currents  corresponding  to  the 
points  P"  and  P,  where  the  straight  line  cuts  the  curve 
PP'P".  For  at  both  of  these  points  the  sum  of  the  drop 
in  potential  through  the  arc  and  that  through  the  resist- 
ance equals  the  E.M.F.  of  the  dynamo.  With  other  cur- 
rents their  sum  would  either  be  too  small  or  too  great. 

With  the  current  corresponding  to  the  point  P  there  is 
stable  equilibrium.  For  if  the  current  should  be  momen- 
tarily increased,  E  will  decrease  by  an  amount  dE,  but  at 
the  same  time  E"  will  increase  by  an  amount  dE"  and 
this  is  greater  than  dE,  so  that  the  two  together  would  re- 
quire an  increase  in  the  E.M.F.  equal  to  dE"  —  dE.  In 
other  words  this  increase  in  current  could  not  be  main- 
tained, if  the  E.M.F.  of  the  dynamo  remained  constant. 

Similar  reasoning  will  show  that  any  momentary  de- 
crease in  the  current  could  not  be  maintained  without  a 
decrease  in  the  E.M.F.  of  the  dynamo,  so  that  P  represents 
a  point  of  stable  equilibrium. 

In  a  similar  way  it  can  be  shown  that  the  point  P" 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES         19 

represents  a  point  of  unstable  equilibrium.  If  all  the  con- 
ditions were  absolutely  constant,  a  small  current  repre- 
sented by  the  abscissa  of  P"  could  exist,  but  any  increase 
in  the  current  would  cause  E  to  decrease  faster  than  E" 
would  increase,  so  that  the  sum  of  the  two  would  be  less 
than  the  E.M.F.  supplied  by  the  dynamo.  This  would 
cause  a  further  increase  in  the  current  and  it  would  con- 
tinue to  increase  until  it  became  equal  to  /,  the  amount 
corresponding  to  the  point  P. 

In  a  similar  way  it  can  be  shown  that  any  decrease  from 
the  amount  corresponding  to  the  point  P"  would  cause  the 
arc  to  be  extinguished,  so  that  P"  represents  a  point  of 
unstable  equilibrium. 

As  the  resistance  in  series  with  the  arc  is  varied  the  slope 
of  the  line  AP  will  change,  but  there  will  be  a  point  where 
there  is  stable  equilibrium  as  long  as  this  line  intersects 
the  curve  PP'P" .  The  limiting  case  will  occur  when  AP 
is  tangent  to  PP'P". 

To  state  mathematically  what  has  been  given  above,  the 
condition  for  stable  equilibrium  is  that 

dE^dE"       ,     u   dE"       _  dE      „ 

-di<-df'    but  -dT  =  R>    •'•  ~Ti<R> 

where  R  is  the  resistance  in  series  with  the  arc. 

For  many  of  the  arcs  it  is  approximately  correct  to  say 

that  E  =  a  +  J,  where  a  and   b   are   constants   for   any 

given  length.     In  such  cases  it  would  follow  that 
dE      b  b    .  „          b  ^  vj 

~Ti=T-    ''•  P<R>  or  J<RI' 

But  E'  =  E  +  RI;     .'.    Ef  >  E  +|- 

That  is,   the  E.M.F.   of   the   dynamo  must  be  greater 


20  THE  ELECTRIC  ARC 

than  the  potential  difference  between  the  terminals  of  the 
arc  plus  the  amount  indicated  by  b/I.  For  example,  if  we 
take  the  values  of  a  and  b  for  the  arc  5  mm.  in  length,  as 
given  by  Mrs.  Ayrton,  we  have  E  =  50  +  64/7.  There- 
fore, for  10  amperes  the  resistance  in  series  with  the  arc 
must  be  more  than  0.64  ohm  and  the  E.M.F.  of  the  dynamo 
must  be  more  than  62.8  volts,  although  the  potential 
difference  between  the  terminals  of  the  arc  is  only  56.4 
volts.  For  5  amperes  the  resistance  must  be  more  than 
2.48  ohms  and  the  E.M.F.  more  than  75.6  volts.  This  is 
quite  in  agreement  with  the  well-known  fact  that  the 
smaller  the  current  the  greater  the  resistance  that  must  be 
in  series  with  it. 

The  energy  used  in  the  resistance  is  E"I.  If  we  again 
assume  that  E  =  a  +  b/I,  we  have  E'  >  E  +  b/I.  From 
this  and  the  equation  E"  =  Ef  —  E  it  can  be  shown  that 
E"I  must  be  greater  than  b.  The  energy  used  in  the  arc 
is  al  +  6,  so  that  the  ratio  of  that  lost  in  the  resistance  to 

that  used  in  the  arc  is  greater  than    ,  ,   ,.     This  becomes 

al  +  b 

smaller  as  7  becomes  larger.  That  is,  the  percentage  of 
energy  necessarily  wasted  in  the  resistance,  when  a  con- 
stant voltage  dynamo  is  used,  is  less  the  greater  the  cur- 
rent. This,  of  course,  does  not  state  what  is  the  best 
current  to  use  in  practice,  for  there  is  still  the  question  as 
to  the  relation  between  the  light  efficiency  of  the  arc  and 
the  current,  a  question  that  will  be  considered  in  the 
chapter  on  photometry. 

It  should  be  noted  that  to  have  stable  equilibrium  it  is 
necessary  that  the  stability  be  not  destroyed  either  be- 
cause of  the  sudden  change  in  potential  difference  between 
the  electrodes  when  the  current  changes,  or  by  the  slower 


ARC   IN  AIR   BETWEEN   CARBON   ELECTRODES         21 

change  considered  above  which  continues  to  occur  for 
several  seconds.  However,  since  the  sudden  change  is 
commonly  less  than  the  slower  one  the  arc  will  be  in  equi- 
librium for  the  sudden  change,  if  it  is  for  the  slower  one. 

Hissing  Arc.  —  With  the  currents  which  are  ordinarily 
used  the  arc  makes  little  or  no  noise.  Such  an  arc  is 
known  as  a  silent  arc."  With  larger  currents  the  arc 
gives  a  hissing  sound  which  becomes  very  loud  and  dis- 
agreeable under  certain  conditions.  Such  an  arc  is  known 
as  a  hissing  arc."  The  voltage  required  is  here  much 
smaller,  as  is  shown  in  the  lower  parts  of  the  curves  in 
Figs.  5  and  6. 

The  correct  explanation  of  this  appears  to  have  been 
given  by  Mrs.  Ayr  ton.1  She  found  that  when  the  crater 
fills  somewhat  symmetrically  the  end  of  the  anode,  the  arc 
is  silent;  when  it  extends  up  the  side,  the  arc  hisses.  More- 
over when  the  arc  is  enclosed  so  that  no  oxygen  can  get  to 
it,  or  is  placed  in  nitrogen,  there  is  no  hissing,  while  there 
is  hissing  when  it  is  in  oxygen.  She  believed  that  the  hiss- 
ing is  due  to  oxygen  coming  in  contact  with  the  crater,  and 
combining  with  the  hot  carbon.  This  chemical  action  is 
supposed  to  cause  a  sudden  decrease  in  the  voltage  and  a 
corresponding  increase  in  current.  The  increase  in  current 
drives  the  air  away  from  the  crater,  and  this  again  causes 
a  higher  voltage  with  decrease  in  current.  Thus,  the  arc 
fluctuates  from  one  condition  to  the  other  with  the  accom- 
panying production  of  sound  waves.2  That  oscillations  in 

1  Journ.  Inst.  Elec.    Eng.,  28,   400;   1899.     Mrs.   Ayrton's  "Electric 
Arc,"  p.  299. 

2  Further  experiments  were  performed  by  the  following: 

Niaudet,  C.  R.,  92,  711;  1881. 

Gime,  Lum.  Elec.,  18,  556;    1885. 

Craveth,  Elec.  World,  19,   195,  and  20,  227;   1892. 


22  THE  ELECTRIC  ARC 

the  current  accompany  the  hissing,  has  been  shown  by 
Firth  and  Rogers,1  and  by  Duddell  and  Marchant.2 

Fall  of  Potential  in  Different  Parts  of  the  Arc.  —  The 
relation  between  the  potential  difference  and  the  current 
through  the  arc  is  so  different  from  that  given  by  Ohm's 
law  that  it  is  a  matter  of  interest  to  examine  the  potential 
in  different  parts  of  the  arc  and  to  find  whether  all  parts 
show  the  same  peculiarity.  To  do  this  some  point  in  the 
arc  must  be  connected  to  a  measuring  instrument  by  a 
conducting  substance,  such  as  a  metallic  wire.  But  any 
wire  placed  in  the  arc  is  immediately  vaporized.  Even  a 
carbon  filament  will  not  answer,  since  it  burns  away 
rapidly.  The  only  conducting  substance  which  can  be 
used  is  a  carbon  pencil.  But  a  carbon  pencil  distorts  the 
form  of  the  arc  and  changes  the  conditions  which  existed 
before  its  introduction.3 

However,  approximate  results  can  be  found  by  this 
method,  and  these  always  show  a  considerable  difference  in 
potential  between  the  anode  and  a  pencil  placed  as  close  to 
it  as  possible.  This  is  called  the  anode  drop.  There  is  a 
similar  difference  in  potential  in  the  neighborhood  of  the 
cathode,  which  is  called  the  cathode  drop.  Between  these 
there  is  a  gradual  change  in  potential  as  in  a  wire.  This 
is  illustrated  by  Fig.  9  taken  from  some  of  Mrs.  Ayrton's 
data,  which  will  be  given  in  the  following  paragraph. 

Measurements  of  these  quantities  have  usually  been 
made  with  either  a  voltmeter  or  a  galvanometer.  This  in- 
volves a  passage  of  electricity  from  the  gas  to  the  explor- 
ing electrode.  As  is  well  known,  there  is  usually  a  large 

1  Phil.  Mag.,  (5),  42,  407;   1896. 

2  Journ.  Inst.  Elec.  Eng.,  28,  78;   1899. 
8  Mrs.  Ayrton's  "  Electric  Arc,"  p.  210. 


ARC   IN  AIR  BETWEEN   CARBON  ELECTRODES         23 


drop  in  potential  at  the  surface  between  a  gas  and  a  solid 
when  a  current  passes  from  one  to  the  other.  Such  a 
drop  here  might  introduce  a  large  error.  But  this  objec- 
tion disappears  when  an  electrometer  is  used  instead  of  a 
voltmeter  and  it  has  been  shown 1  that  the  two  instruments 
give  the  same  readings  when  used  to  measure  the  potential 
in  the  arc.  It,  therefore,  seems  safe  to  assume  that  in  this 

60 


50 


40 


20 


10 


ANODE 


CA 


THODE 


1234 

DISTANCE  FROM  ANODE 
FIG.  9. 


case  the  exploring  carbon  becomes  so  hot  and  the  vapor  of 
the  arc  is  such  a  good  conductor  that  there  is  no  appreci- 
able drop  in  potential  between  the  pencil  and  the  gas 
about  it. 

This  fact  is  not  in  agreement  with  an  experiment  of 
Fleming's.2  He  was  not  able  to  find  any  current  flowing 
through  a  circuit  from  an  exploring  pencil  to  the  cathode. 
If  this  were  correct,  it  would  not  be  possible  to  measure 


1  Phys.  Rev.,  19,  119;   1904. 

3  Proc.  Roy.  Soc.,  47,  123;  1890. 


24  THE  ELECTRIC  ARC 

the  cathode  drop  with  a  voltmeter  or  galvanometer,  a 
measurement  which  has  been  made  many  times.  Probably 
in  Fleming's  experiment  the  pencil  was  not  inserted  far 
enough  into  the  arc  to  become  thoroughly  hot.  If  the 
pencil  was  comparatively  cold,  it  would  be  quite  possible 
to  make  the  observations  as  they  were  made  by  him. 

Measurements  of  the  anode  and  cathode  drops  have 
been  made  by  Lecher,1  Uppenborn,2  Luggin,3  and  Fleming.4 
But  the  most  accurate  work  is  that  given  by  Mrs.  Ayrton,5 
who  gives 


as  the  equation  for  the  anode  drop  when  both  carbons  are 
solid,  where  Ea  is  the  anode  drop,  I  the  current,  and  /  the 
length  of  the  arc  in  millimeters.  She  also  gives 


where  Ec  is  the  cathode  drop.  When  cored  carbons  are 
used  she  found  that  the  potential  difference  is  in  general 
two  or  three  volts  lower  than  when  both  carbons  are  solid, 
and  that  the  cathode  drop  is  about  i  volt  lower. 

The  direct  measurement  of  the  fall  of  potential  through 
the  gaseous  part  of  the  arc  cannot  be  satisfactorily  ac- 
complished. It  requires  the  introduction  into  the  arc  of 
two  carbon  pencils,  and  this  distorts  the  arc  so  much  as 
to  make  nearly  valueless  any  measurements  which  may  be 

1  Centralbl.  f.  Elektrot.,  10,  48;    1888.     Wied.  Ann.,  33,  609;   1888. 

2  Centralbl.  f.  Elektrot.,  10,  102;   1888. 

3  Centralbl.  f.  Elektrot.,  10,  567;   1888. 

4  Proc.  Roy.  Soc.,  27,  118;   1894. 

6  Mrs.  Ayrton's  "Electric  Arc,"  p.  222. 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES         25 

- — 

made.  A  few  measurements  were  made  by  myself1  in  this 
manner,  and  the  electric  force  was  found  to  be  2.34  volts 
per  millimeter  for  a  current  of  10  amperes,  but  no  great 
accuracy  can  be  claimed  for  these  measurements. 

It  has  generally  been  assumed  that  the  electric  force 
could  be  found  by  observing  the  increase  in  voltage  when 
the  length  of  the  arc  was  increased  and  that  it  is  equal  to 
the  ratio  of  the  increase  in  voltage  to  the  increase  of  length, 
the  current  remaining  constant.  This  would  be  correct, 
if  changing  the  length  of  the  arc  did  not  change  either  the 
anode  or  cathode  drop,  but  Mrs.  Ayrton  found  that  such 
a  change  did  exist  in  the  anode  drop.  However,  we  can 
arrive  at  a  fair  approximation  by  following  this  method 
and  making  a  correction  for  this  change.  If,  therefore, 
we  assume  the  equation  for  E,  given  on  page  14,  and  that 
for  the  anode  drop  given  on  page  24,  we  find  the  value  for 
the  electric  force  to  be  2.07  +  7-44//.  This  will  give  a 
value  of  2. Si  volts  per  millimeter  when  the  current  is 
10  amperes,  which  is  not  far  from  that  found  experimentally 
by  myself. 

We  thus  see  that  the  peculiar  relation  which  exists  in 
the  arc  between  voltage  and  current  must  be  ascribed  to 
all  of  the  three  parts.  The  voltage  of  each  part  decreases 
when  the  current  increases.  The  decrease  in  the  anode 
drop  is  greater  than  that  in  the  cathode  drop,  while  the 
decrease  in  the  drop  of  potential  through  the  gaseous  part 
of  the  arc  depends,  of  course,  on  the  length  of  the  arc. 
However,  with  arcs  more  than  6  mm.  long  more  than  one- 
half  of  the  total  decrease  occurs  in  the  gaseous  part. 

Counter  E.M.F.  of  the  Arc.  —  As  has  been  stated  Edlund 
found  that  the  "apparent  resistance"  of  the  arc  equals 

1  Phys.  Rev.,  19,  122;   1904. 


26  THE  ELECTRIC  ARC 

m  +  ril,  where  m  and  n  are  constants  and  /  is  the  length  of 
the  arc.  He  believed  that  the  first  term  of  this  expression 
was  due  to  a  counter  E.M.F.  Others  did  not  agree  with 
him,  and  the  discussion  then  started  has  continued  to  the 
present  time.  This  discussion  has  been  carried  on  partly 
because  there  have  been  differences  of  opinion  as  to  facts, 
but  more  often  because  there  has  been  no  agreement  as  to 
the  meaning  of  the  terms  used.  In  the  beginning  there 
was  too  little  known  to  admit  of  any  clear  definition  of  the 
terms,  "  counter  E.M.F. "  and  "  resistance/7  and  though 
there  have  since  been  clear  definitions  of  these  terms,  there 
has  been  no  general  agreement  as  to  their  use,  and  often  no 
good  understanding  of  how  others  were  using  the  terms. 

It  would  appear  that  the  term  "  counter  E.M.F."  should 
mean  the  same  when  applied  to  the  arc  as  when  applied  to 
a  motor  or  a  storage  cell.  In  those  cases  we  find:  first, 
that  the  potential  difference  between  the  terminals  of  a 
cell  or  motor  does  not  obey  Ohm's  law;  secondly,  that 
there  is  an  E.M.F.  remaining  after  the  impressed  E.M.F. 
has  been  removed  and  that  this  is  of  sufficient  magnitude 
to  account  for  the  deviation  from  Ohm's  law;  and  thirdly, 
that  in  the  majority  of  cases  the  electrical  energy  is  changed 
into  something  besides  heat  energy. 

In  the  arc  only  the  first  of  these  properties  is  found  to 
exist.  In  fact  the  arc  deviates  from  Ohm's  law  much  as 
other  forms  of  discharge  through  gases  deviate,  where  the 
expression  "counter  E.M.F."  has  never,  I  believe,  been 
applied. 

In  the  beginning  of  the  investigation  on  the  arc  it  was 
not  known  that  this  was  the  only  point  of  similarity  be- 
tween the  arc  and  a  cell,  and  writers  using  the  word  no 
doubt  had  in  mind  a  counter  E.M.F.  identical  with  that  of 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES         27 

~~~—~- 

the  cell.  Later  writers  have  used  the  term  merely  to  mean 
that  the  potential  difference  of  the  arc  deviates  from 
Ohm's  law  in  a  definite  manner,  and  have  so  denned  it. 
Yet  no  one  seems  to  have  pointed  out  that  the  meaning 
of  the  term  as  denned  by  Duddell,  for  example,  is  not  the 
same  as  the  meaning  which  Edlund  had  in  mind,  nor  the 
meaning  generally  given  to  the  term  in  physics.  This  has 
led  to  more  or  less  confusion  in  what  has  been  written  on 
the  subject  during  the  past  few  years.  For  example,  one 
occasionally  sees  the  statement  that  it  has  at  last  been 
definitely  shown  that  there  is  a  counter  E.M.F.  in  the 
arc.  The  fact  is  that  on  the  one  hand  it  has  neither  re- 
cently nor  at  any  other  time  been  shown  that  the  arc  has 
more  than  the  first  of  the  three  peculiarities  mentioned 
above,  and  on  the  other  it  has  never  been  doubted  but  that 
there  was  this  one  point  of  similarity  between  the  arc  and 
the  cell. 

The  methods  which  have  been  used  to  test  the  existence  of 
a  counter  E.M.F.  may  be  divided  into  two  general  classes: 
First,  methods  which  attempt  to  find  a  counter  E.M.F. 
by  measuring  the  resistance  of  the  arc;  and  secondly, 
those  attempting  to  find  it  by  measuring  the  E.M.F.  re- 
maining between  the  carbons  after  the  impressed  E.M.F. 
has  been  removed,  or  what  we  may  call  the  residual  E.M.F. 
of  the  arc. 

Those  who  attacked  the  problem  by  measuring  the  re- 
sistance of  the  arc  have  assumed  that  the  counter  E.M.F. 
was  the  difference  between  the  potential  difference  at  the 
terminals  of  the  arc  and  that  part  of  it  which  appeared  to 
obey  Ohm's  law.  In  other  words  that  £'  =  E  -  RI, 
where  E'  is  the  counter  E.M.F. ,E  the  potential  difference  at 
the  terminals,  R  the  resistance  of  the  arc,  and  /  the  current. 


28  THE  ELECTRIC  ARC 

Meaning  of  "  Resistance  of  the  Arc."  —  We  find,  how- 
ever, that  "resistance  of  the  arc"  has  meant  four  different 
things  with  different  experimenters,  and  with  these  differ- 
ent meanings  there  are  corresponding  differences  in  what 
is  meant  by  counter  E.M.F. 

First  of  all  it  has  been  used  to  mean  the  ratio  between 
the  potential  difference  at  the  terminals  and  the  current. 
This,  however,  has  usually  been  called  the  "  apparent  re- 
sistance." 

Secondly,  it  has  been  used  to  mean  the  term  nl  in  the 
expression  r  =  m  -\-  nl,  which  was  used  by  Edlund,  namely, 
the  part  of  the  apparent  resistance  which  was  proportional 
to  the  length  of  the  arc.  This  Edlund  called  the  "  true 
resistance." 

At  a  later  time  it  was  used  to  mean  the  ratio  between  a 
small  increase  in  E  and  the  corresponding  increase  in  7,  or 
what  we  may  call  dE/dl.  An  approximation  to  this  was 
made  by  those  who  used  some  modification  of  the  Wheat- 
stone  bridge. 

Finally,  it  was  pointed  out  by  Luggin1  that  any  change 
in  the  current  through  the  arc  produced  a  corresponding 
change  in  both  the  vapor  of  the  arc  and  the  shape  of  the 
carbon,  so  that  one  does  not  have  the  same  arc  after  the 
current  has  been  increased  as  before.  The  methods  which 
are  modifications  of  the  Wheatstone  bridge  do  not  cor- 
rectly measure  either  the  resistance  of  the  arc  in  its  first 
condition,  nor  its  resistance  after  the  current  has  been  in- 
creased. This  difficulty  has  been  clearly  stated  by  Mrs. 
Ayrton,2  Duddell3  and  others.  They  have,  therefore,  de- 

1  Centralbl.  f.  Elektrot.,  10,  567;   1888. 

2  Mrs.  Ayrton's  "  Electric  Arc,"  p.  400. 

3  Phil.  Trans.,  203,  A,  306,  1904. 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES         29 

fined  the  true  resistance  of  the  arc  as  the  ratio  between  a 
small  change  in  potential  difference  and  the  corresponding 
change  in  the  current,  when  the  change  is  made  so  small,  or 
for  so  short  a  time,  that  the  condition  of  the  arc  itself  does 
not  vary.  In  other  words  the  resistance  as  thus  defined  is 
the  partial  derivative  of  the  potential  difference  with  re- 
spect to  the  current  which  we  shall  indicate  by  dE/dl. 

This  would  undoubtedly  be  the  correct  way  of  defining 
the  resistance,  if  it  were  not  for  the  doubt  which  must 
exist  in  one's  mind  as  to  whether  it  is  possible  to  have  a 
change  in  current  without  having  a  change  in  the  con- 
dition of  the  arc.  If  the  current  in  the  arc  is  carried  by 
ions,  as  we  have  reason  to  believe,  it  is  not  possible  to 
change  the  current  without  changing  either  the  number  of 
the  ions  or  their  velocity.  In  either  case  there  would  be  a 
change  in  the  condition  of  the  gas.  However,  this  defi- 
nition may  properly  be  considered  as  giving  a  limiting  con- 
dition toward  which  a  close  approximation  may  be  made, 
although  it  would  be  better  to  avoid  the  use  of  the  word 
"  resistance  "  entirely  when  speaking  of  the  arc.  It  is  com- 
monly avoided  when  speaking  of  the  discharge  of  elec- 
tricity through  vacuum  tubes,  and  there  is  the  same  reason 
for  avoiding  it  here. 

If  we  pass  to  other  methods  of  attacking  the  problem 
we  find  that  Swendler1  gave  the  value  of  the  counter 
E.M.F.  as  2  volts,  but  since  he  did  not  divulge  his  method 
of  arriving  at  this  conclusion,  we  are  unable  to  judge  of 
the  importance  of  his  work. 

As  far  as  we  know  the  first  experimenter  to  use  a  method 
different  from  that  of  Edlund's  was  von  Lang2  who  en- 

1  Lond.  Elec.,  2,  107  and  117;   1879. 

2  Centralbl.  f.  Elektrot.,  7,  443;    1885.     Wied.  Ann.,  26,  145;   1885. 


30  THE  ELECTRIC  ARC 

deavored  to  measure  the  resistance  of  the  arc  by  a  modi- 
fication of  the  Wheatstone  bridge,  shown  in  Fig.  10.  Two 
arcs  L!  and  L%  are  operated  by  a  battery  B^Bz.  This  cir- 
cuit is  connected  to  the  Wheatstone  bridge  at  B  and  A. 
If  all  the  resistances  are  known  except  those  in  the  arcs, 
their  resistances  may  be  computed.  It  is  evident  that 
there  is  great  difficulty  in  balancing  a  bridge  with  this 
arrangement.  It  is  in  fact  surprising  that  von  Lang  was 


FIG.  10. 

able  to  give  any  definite  value  whatever  to  the  resistance 
as  thus  found.  He  found  the  resistance  to  be  1.82  ohms 
and  concluded  that  the  counter  E.M.F.  was  38.9  volts. 
This  method  gave  approximately  the  value  of  the  resist- 
ance as  defined  the  third  way,  namely,  dE/dl. 

Attempts  were  then  made  to  find  the  resistance  when 
the  change  in  the  current  was  made  much  smaller,  that  is,1 
to  get  the  value  indicated  by  the  expression  dE/dl.  Arons 
attempted  to  do  this  by  using  a  different  modification  of 
the  Wheatstone  bridge.  The  arc  with  the  battery  produc- 

1  Wied.  Ann.,  30,  95;   1887. 


ARC  IN  AIR  BETWEEN   CARBON  ELECTRODES        31 

ing  it  was  used  as  one  branch  of  the  Wheats  tone  bridge. 
Instead  of  the  battery  ordinarily  used  with  the  bridge  a 
transformer  was  used  and  instead  of  a  galvanometer  a 
dynamometer.  The  three  arms  of  the  bridge  were  ad- 
justed until  no  current  was  shown  by  the  dynamometer. 
The  resistance  of  the  arc  could  then  be  determined.  The 
resistance  was  found  to  be  approximately  2  ohms  and  the 
counter  E.M.F.  40  volts.  Luggin1  used  a  different  modi- 
fication of  the  bridge  and  Firth2  still  another,  both  getting 
results  similar  to  those  of  Arons. 

"Negative  Resistance." -— In  1895  Ayrton3  concluded 
from  the  result  of  a  few  simple  experiments  that  the  re- 
sistance of  the  arc  was  negative.  What  he  measured  was 
dE/dl.  It  had  been  previously  pointed  out  by  Luggin 
that  this  quantity  was  negative,  and  it  has  since  been 
shown  even  more  clearly  by  the  curves  given  by  Mrs. 
Ayrton.4  If  one  is  to  define  resistance  as  meaning  dE/dl, 
there  is  no  question  but  that  the  resistance  of  the  arc  is  a 
negative  quantity,  but  of  all  the  uses  of  the  word  this  is 
perhaps  the  least  justifiable,  and  to  speak  of  a  negative 
resistance  is,  to  say  the  least,  misleading. 

The  word,  resistance,  means  primarily  something  which 
hinders  the  movement  of  some  object.  An  electrical  re- 
sistance means  something  which  hinders  the  flow  of  an 
electric  current,  and  the  most  natural  meaning  of  the  ex- 
pression ''negative  resistance"  would  be  something  which 
helps  the  flow  of  the  current.  It  is  needless  to  say  that 
the  resistance  of  the  arc  does  not  help  the  flow  of  current. 

1  Centralbl.  f.  Elektrot,  10,  567;   1888. 

2  Mem.  and  Proc.  Manchester  Lit.  and  Phil.  Soc.,  (4),  9,  139;  1895. 

3  Mrs.  Ayrton's  "  Electric  Arc,"  p.  75. 

4  Mrs.  Ayrton's  "  Electric  Arc,"  p.  113. 


32  THE   ELECTRIC   ARC 

Firth  and  Rogers1  superimposed  an  alternating  current 
on  the  direct  current  through  the  arc,  and  the  resistance  of 
the  arc  to  this  alternating  current  was  taken  as  its  resist- 
ance. Frequencies  between  7  and  250  complete  alterna- 
tions per  second  gave  the  same  resistance.  They,  there- 
fore, believed  that  the  changes  in  the  current  were  so 
rapid  that  there  were  no  corresponding  changes  in  the 
arc.  The  value  of  the  resistance  which  they  found  varied 
much  with  different  carbons  and  with  different  currents. 
Values  ranging  from  2  to  —  2  ohms  are  given  by  them. 
The  corresponding  values  of  the  counter  E.M.F.  were  in 
the  neighborhood  of  40  volts. 

Following  the  investigation  of  Firth  and  Rogers  was  a 
careful  examination  of  the  counter  E.M.F.  and  resistance 
by  Duddell.2  His  principal  advance  over  the  work  of 
others  consisted  first  in  devising  a  method  by  which  one 
could  test  whether  the  arc  remained  constant  during  the 
change  in  current  or  not,  and  secondly,  in  using  much 
higher  frequencies  than  those  which  had  previously  been 
used. 

To  decide  whether  the  arc  changed  any  or  not  he  im- 
posed a  small  alternating  current  on  the  direct  current 
which  was  passing  through  the  arc,  and  determined  whether 
this  alternating  current  was  in  phase  with  its  E.M.F.  or 
not.  Ordinarily,  when  an  alternating  current  is  thus 
used,  it  lags  behind  its  E.M.F.  Duddell  assumed  that  if 
the  two  were  in  phase  the  condition  of  the  arc  had  not 
changed  during  the  change  in  current.  He  found  that  for 
low  frequencies  with  solid  carbons  the  oscillations  were 
1 80  degrees  out  of  phase,  and  that  to  have  the  two 

1  Phil.  Mag.,  (5),  42,  407;   1896. 

2  Phil.  Trans.,  203,  A,  305;   1904. 


ARC  IN  AIR  BETWEEN   CARBON  ELECTRODES        33 

in  phase  with  such  carbons  it  was  necessary  to  have 
frequencies  of  100,000  or  more  per  second.  For  cored 
carbons  26,000  alternations  per  second  were  needed. 

When  the  alternating  current  was  in  phase  with  its 
E.M.F.  the  ratio  between  the  E.M.F.  and  the  current  was 
taken  as  the  "true  resistance"  of  the  arc,  and  the  counter 
E.M.F.  was  found  from  the  formula  E'  =  E  —  RI.  The 
value  of  Er  as  found  by  him  varied  from  11.2  to  18.5  volts 
with  different  currents  and  different  carbons. 

"  Forward  E.M.F."  —  He  also  endeavored  to  find  the 
part  of  the  arc  where  this  counter  E.M.F  was  situated. 
For  this  purpose  he  inserted  an  exploring  pencil  in  the 
arc  and  found  the  potential  difference  between  this  and 
the  anode,  both  for  the  direct  and  for  the  superimposed 
alternating  current.  From  this  data  he  computed  the 
counter  E.M.F.  near  the  anode,  using  the  same  method 
as  that  given  above.  This  he  found  to  be  approximately 
17  volts.  A  similar  set  of  readings  gave  a  "forward 
E.M.F."  near  the  cathode  of  6  volts,  the  two  accounting 
for  the  ii  volts  which  were  found  in  this  particular  case 
for  the  whole  arc. 

This  again  is  a  use  of  words  which  in  one  sense  is  entirely 
correct,  and  yet  is  entirely  misleading.  Duddell  un- 
doubtedly found  the  value  of  E  —  RI  near  the  cathode  to 
be  a  negative  quantity,  and  since  he  had  called  this  a 
"  counter  E.M.F."  when  it  was  positive,  it  is  not  surprising 
that  it  should  be  called  a  "forward  E.M.F."  when  it  was 
negative.  Yet  to  do  so  gives  one  the  impression  that  there 
is  an  E.M.F.  at  the  cathode  of  the  order  of  6  volts,  which 
changes  some  other  form  of  energy  into  electrical  energy. 
In  reality  there  is  no  reason  whatever  to  suppose  that 
there  is  any  such  E.M.F.  at  that  point.  All  that  DuddelTs 


34  THE  ELECTRIC  ARC 

experiment  showed  was  that  dE/dl  was  greater  than  E/I 
between  the  gas  of  the  arc  and  the  cathode.  In  other 

words,  that  the  form  of  the 
curve  showing  the  relation 
between  the  cathode  drop 
and  the  current  was  that 
shown  in  Fig.  n.  This  is 
the  same  kind  of  a  curve 
that  one  finds  when  examin- 
ing the  relation  between 
the  potential  difference  and 

the  current  for  discharge  produced  by  Rontgen  rays.  No 
one  ever  speaks  of  a  ''forward  E.M.F."  with  such  discharge 
and  there  would  appear  to  be  no  more  reason  for  using 
that  expression  in  connection  with  the  arc. 

Pollock1  explained  this  "forward  E.M.F."  of  Duddell's 
as  being  due  to  the  tendency  of  a  hot  cathode  to  send 
negative  ions  out  from  it.  This  tendency  undoubtedly 
exists  and  in  this  case  it  would  assist  the  flow  of  current, 
but  if  it  assisted  enough  to  produce  a  forward  E.M.F., 
there  would  be  a  rise  in  potential  at  the  surface  of  the 
cathode  instead  of  a  drop,  and  a  change  of  heat  energy 
into  electrical  energy,  while  in  reality  we  find  there  a  change 
in  the  opposite  direction.  It  is  altogether  possible  that 
this  change  of  energy  would  be  greater,  if  the  emission  of 
negative  ions  did  not  exist,  but  we  have  no  evidence  that 
the  difference  between  what  the  cathode  drop  would  be 
and  what  it  is,  is  the  same  in  amount  as  the  "forward 
E.M.F."  which  was  found  by  Duddell. 
Heinke2  computed  the  counter  E.M.F.  from  observa- 

1  Phil.  Mag.,  (6),  18,  229;    1909. 

2  Verb.  d.  V.  z.  Beford.  d.  Gewerbfliesses,  83,  403;  1904. 


ARC  IN  AIR  BETWEEN   CARBON  ELECTRODES 

tions  made  on  the  whistling  arc.  His  method  was  in 
principle  the  same  as  Duddell's,  but  the  alternating  current 
was  produced  by  the  arc  itself,  and  not  by  a  separate 
dynamo.  The  current  in  a  whistling  arc  is  equivalent 
to  a  small  alternating  current  superimposed  on  a  direct 
current.  He  says  concerning  it  that  "only  about  one- 
eighth  of  the  observed  potential  difference,  namely,  in  this 
case,  about  6  volts,  was  used  in  overcoming  the  ohmic 
resistance  of  the  arc,  while  the  remainder,  namely,  about 
40  volts,  is  to  be  considered  a  polarized  potential  differ- 
ence, or  counter  E.M.F.  (cathode  and  anode  drop  in 
potential)." 

We  may  sum  up  these  results  by  saying  that  they  show 
that  the  potential  difference  between  the  terminals  of  the 
arc  varies  when  the  current  is  varied  in  much  the  same 
way  as  the  potential  difference  between  the  terminals  of 
the  cell  of  a  storage  battery,  but  they  show  nothing,  of 
course,  concerning  the  phenomena  occurring  after  the  im- 
pressed E.M.F.  is  removed.  For  this  purpose  we  must 
examine  the  second  group  of  experiments. 

Residual  E.M.F.  —  The  second  method  of  testing  for  a 
counter  E.M.F.  in  the  arc  was  to  measure  the  residual 
E.M.F.  after  the  impressed  E.M.F.  was  removed.  There 
is  no  question  of  the  meaning  of  terms  involved  in  these 
measurements  and  there  is  apparently  no  great  experi- 
mental difficulty,  and  yet  there  has  perhaps  been  as  great 
disagreement  among  experimenters  concerning  such  an 
E.M.F.  as  concerning  any  question  in  physics. 

Edlund1  not  only  suggested  a  counter  E.M.F.  as  ex- 
plaining the  relation  which  he  found  between  the  potential 
difference  at  the  terminals  of  the  arc  and  its  length,  but 

1  Pogg.  Ann.,  134,  250  and  337;   1868. 


36  THE  ELECTRIC  ARC 

endeavored  to  find  a  corresponding  residual  E.M.F.  He 
passed  a  current  from  a  number  of  cells  through  the  vapor 
of  the  arc  after  the  impressed  E.M.F.  had  been  removed, 
passing  it  first  in  the  direction  of  the  supposed  E.M.F. 
and  then  in  the  opposite  direction.  He  found  the  current 
in  the  first  direction  to  be  the  greater.  To  compare  the 
E.M.F.'s  in  the  two  cases  he  eliminated  the  resistance  of 
the  circuit  by  using  Ohm's  law,  but  Ohm's  law  does  not  at 
all  apply  to  the  case  of  discharge  through  hot  vapors,  and 
the  supposition  in  this  case  introduced  a  very  large  error. 
He  was  led  to  believe  that  the  counter  E.M.F.  was  equiva- 
lent to  10  or  15  Bunsen  cells. 

But  eight  years  before  this  Wild1  had  measured  this 
same  quantity  by  throwing  the  arc  with  a  double-throw 
switch  from  the  batteries  to  a  high  resistance  galvanometer. 
He  was  not  able  to  determine  the  E.M.F.  accurately,  be- 
cause the  resistance  of  the  vapor  between  the  carbons  was 
not  known  to  him,  but  he  concluded  that  it  was  more  than 
100  times  as  great  as  the  E.M.F.  produced  by  a  copper- 
German  silver  couple  having  the  same  difference  of  tem- 
perature at  its  terminals.  This  statement,  indefinite 
though  it  is,  is  more  accurate  than  any  statement  of  resid- 
ual E.M.F.  made  for  several  decades  thereafter. 

After  Edlund's  experiments  there  was  a  series  of  obser- 
vations by  different  experimenters,  giving  all  kinds  of 
values  from  zero  to  two  volts.  The  fact  that  many  of  the 
earlier  experimenters  found  no  residual  E.M.F.  is  less  sur- 
prising, since  they  were  looking  for  one  comparable  with 
the  supposed  counter  E.M.F.  of  the  arc,  and  we  can  now 
say  definitely  that  there  is  none  of  this  order  of  magnitude. 
But  that  some  of  the  later  experimenters  should  have 

1  Pogg.  Ann.,  in,  624;   1860. 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES 

differed  so  decidedly  as  to  a  small  residual  E.M.F.  is  hard 
to  understand. 

Lecher,1  Luggin,2  Corbino  and  Liga3  concluded  that 
there  was  no  residual  E.M.F.  Strenger4  concluded  that 
if  there  was  one  it  was  small  compared  with  10  volts. 
Hertzfeld5  thought  at  first  that  he  had  found  one,  but 
afterwards  concluded  that  the  observed  effects  were  due  to 
thermojunctions  outside  the  arc.  Le  Roux6  found  a 
residual  E.M.F.  but  did  not  give  its  magnitude. 

Arons7  thought  that  the  vapor  remaining  between  the 
carbons  after  the  impressed  E.M.F.  was  removed  was  not 
conducting  for  small  voltages,  and  that  it  was  necessary  to 
apply  1 8  volts  in  order  to  get  any  current  through  it. 

Granqvist8  showed  that  Arons'  failure  to  get  a  current 
with  lower  voltages  was  due  to  using  a  non-sensitive  galva- 
nometer. Granqvist  himself  was  able  to  pass  a  current 
from  one  Daniell  cell.  His  method  was  similar  to  Ed- 
lund's,  except  that  he  used  a  rotating  switch  which  closed 
the  galvanometer  circuit  0.0009  second  after  the  main  cir- 
cuit was  broken.  He  also  assumed  Ohm's  law  to  hold,  but 
his  voltages  were  much  smaller  than  Edlund's,  so  that  the 
error  which  was  introduced  in  his  calculations  was  much 
smaller.  He  found  a  residual  E.M.F.  of  0.23  volt  in  the 
opposite  direction  to  that  of  the  impressed  E.M.F. 

Blondel,9  using  a  method  almost  identical  with  that  of 

1  Wien.  Sitzungsber.,  95,  2  A,  992;   1887. 

2  Wien.  Sitzungsber.,  98,  2  A,  1192;   1889. 

3  Monash,  Der  Elektrische  Lichtbogen,  p.  134. 

4  Wied.  Ann.,  45,  33;   1892. 

5  Wied.  Ann.,  62,  435;    1897. 

6  Lum.  Elec.,  3,  285,  and  C.  R.,  92,  709;   1881. 

7  Wied.  Ann.,  57,  185;   1896. 

8  Beib.,  22,  243;   1898. 

8  Lond.  Elec.,  39,  615;  1897. 


38  THE   ELECTRIC  ARC 

Granqvist,  concluded  that  there  was  no  E.M.F.  1/600 
second  after  the  arc  was  interrupted  as  great  as  0.16  volt. 
He  used  both  solid  and  cored  carbons,  long  and  short  arcs, 
changed  the  time  between  the  disconnection  of  the  arc 
from  the  main  circuit  and  the  connection  to  the  galva- 
nometer circuit,  and  in  other  ways  varied  the  conditions 
as  far  as  possible. 

On  the  other  hand  Hotchkiss,1  using  an  oscillograph  hav- 
ing a  period  of  0.0002  second,  found  indications  of  an 
E.M.F.  This  was  less  than  0.66  volt,  but  was  still  clearly 
discernible.  Mitkiewicz2  found  a  residual  E.M.F.  of  from 
1.5  to  2  volts.  Becknell3  found  an  appreciable  E.M.F. 
existing  for  several  seconds  after  the  impressed  E.M.F. 
was  removed.  He  determined  the  amount  by  balancing  it 
against  a  known  potential  difference  by  means  of  a  sen- 
sitive galvanometer.  The  values  which  he  found  are 
shown  in  Fig.  12.  When  the  arc  was  first  extinguished  the 
resistance  was  small,  but  increased  very  rapidly  with  the 
time.  He  showed  that  the  residual  E.M.F.  was  not  due  to 
the  thermal  junctions  outside  the  arc. 

It  is  very  difficult  to  reconcile  the  work  of  Blondel  with 
that  of  the  others.  Furthermore,  it  is  hard  to  see  how  it 
could  be  otherwise  than  that  there  is  such  a  residual  E.M.F. 
It  was  shown  by  Dubs4  and  Olivette5  that  the  current  flows 
from  a  cooler  carbon  to  one  very  hot.  This  may  amount 
to  several  volts.  All  the  phenomena  observed  by  Becknell 
are  such  as  would  be  expected  from  the  difference  in  tem- 

1  Trans.  Amer.  Phys.  Soc.,  2;  1901. 

2  Science  Abs.,  7,  360;  1903.     Beib.,  27,  465;   1903. 
8  Phys.  Rev.,  21,  181;   1905. 

4  Centralbl.  f.  Elektrot.,  10,  749;   1888. 

5  Lond.  Elec.  Rev.,  31,  728;  1892. 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES        39 

perature  of  the  carbons.  There  is  probably  a  very  small 
area  on  the  cathode  which  is  as  hot  as  the  anode,  so  that 
when  the  impressed  E.M.F.  is  first  removed  the  difference 
in  temperature  between  the  electrodes  is  small.  The  area 
of  this  high  temperature  on  the  cathode  is  small.  It  will. 


0.  6 


0.5 


20.3 


|o.2| 

LJ 

tr 


\ 


0.1 


TIME  IN  SECONDS 
FlG.    12. 


therefore,  cool  more  quickly  than  the  anode,  so  that  the 
difference  in  temperature  between  the  electrodes  at  first 
increases.  This  would  correspond  to  the  increase  in  the 
residual  E.M.F.  observed  by  Becknell.  The  observed 
residual  E.M.F.  is  in  the  direction  corresponding  with  this 
view,  since  the  anode  is  hotter  than  the  cathode  after  the 
arc  is  extinguished. 


40  THE   ELECTRIC   ARC 

This  explanation  can  be  tested  by  changing  in  some  way 
the  temperature  of  the  electrodes.  The  greatest  change  in 
the  residual  E.M.F.  may  be  expected  when  the  anode  is 
cooled,  for  under  ordinary  conditions  this  is  hotter  than 
the  cathode,  and  when  cooled  we  should  expect  the  E.M.F. 
to  be  diminished  or  reversed.  Such  a  test  was  made  by 
myself.1  The  anode  was  cooled  by  three  different  methods. 
In  the  first  the  anode  was  a  hollow  carbon  through  which 
water  could  be  passed.  In  the  second  a  carbon  arc  was 
placed  in  a  vacuum,  where  the  anode  does  not  become 
heated  as  much  as  in  air.  With  both  of  these  methods  the 
residual  E.M.F.  was  much  smaller  than  when  an  ordinary 
.arc  between  carbons  in  air  is  used. 

In  the  third  method  mercury  was  used  for  the  anode 
with  the  arc  in  a  vacuum.  Here  the  temperature  of  the 
anode  was  lower  than  in  either  of  the  other  cases  and  the 
residual  E.M.F.  was  reversed.  These  results  were  all  in 
harmony  with  the  idea  that  the  residual  E.M.F.  of  the  arc 
is  due  to  the  difference  in  temperature  of  the  terminals. 

Temperature  of  the  Arc.  —  There  is  at  present  no  method 
of  determining  the  exact  temperature  of  the  arc.  The 
temperature  of  the  vapor  is  not  even  known  approximately. 
All  that  one  can  say  about  the  vapor  is  that  the  most  re- 
fractory substances  may  be  vaporized  in  it.  Since  this  is 
so,  the  temperature  of  the  vapor  must  certainly  be  hotter 
than  that  of  the  carbon  electrodes.  Moissan2  found  that 
with  large  currents  more  refractory  elements  were  vaporized 
than  with  small,  and  concluded  that  with  such  currents 
higher  temperatures  were  reached.  This  cannot  be  consid- 
ered proven,  since  the  greater  power  to  vaporize  may  have 

1  Phys.  Rev,  ,30,  311;  1910. 

2  C.  R.,  116,  1429;  1893,  and  119,  776;  1894. 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES        41 

been  due  to  the  greater  volume  of  the  hot  gas,  not  to  its 
higher  temperature. 

We  have  somewhat  more  definite  knowledge  concerning 
the  temperature  of  the  carbon  terminals  of  the  arc,  and 
this  is  what  is  commonly  meant  when  reference  is  made  to 
the  temperature  of  the  arc.  Yet  all  attempts  to  find  this 
temperature  make  use  of  some  assumption  which  cannot 
be  strictly  verified.  With  one  exception  all  experimenters 
have  made  use  of  observations  on  the  radiation  from  the 
carbons  and  have  computed  from  these  the  temperature  by 
means  of  some  formula.  The  majority  of  these  formulae 
have  been  empirical  and  while  they  have  been  found  to 
hold  for  lower  temperatures,  there  is  no  proof  that  they 
also  hold  for  higher  ones.  This  is  certainly  true  for  those 
used  in  the  earlier  work.  Thus  Becquerel 1  in  1833  assumed 
that  L  =  a  (eb(T~e}  -  I))  where  L  is  the  intensity  of  the  red 
light,  e  the  absolute  temperature  of  the  surrounding  body, 
T  the  temperature  of  the  luminous  body,  and  a  and  b  con- 
stants depending  on  the  nature  of  the  body.  From  this 
he  computed  the  temperature  of  the  arc  to  be  2070°  C. 

Rosetti,2  using  a  somewhat  more  complicated  formula 
found  the  temperature  of  the  anode  to  lie  between  2400° 
and  2900°  C.,  and  that  of  the  cathode  between  2138°  and 
2530°  C.  Other  formulae  were  given  by  Le  Chatelier,3 
Wilson  and  Gray,4  Dewar,5  and  Petavel.6  Their  results 
ranged  from  the  value  given  above  by  Becquerel  to 
6000°  C.,  the  value  given  by  Dewar.  This  last  was  com- 

1  Ann.  de.  Chem.  et  Phys.,  (3),  68,  49;   1833. 

2  Nuovo  Cim.,  (3),  6,  202;   1879,  and  7,  138  and  185;   1880. 

3  Journ.  de  Phys.,  (3),  i,  185;   1892. 

4  Proc.  Roy.  Soc.,  58,  24;  1895. 

5  Proc.  Roy.  Soc.,  30,  85;  1880. 

6  Phil.  Trans.,  191  A.,  515;   1898. 


42  THE  ELECTRIC  ARC 

puted  on  the  assumption  that  radiation  varies  as  the 
square  of  the  temperature,  an  assumption  which  is  quite 
incorrect. 

Violle1  is  the  only  experimenter  who  has  made  a  de- 
termination of  the  temperature  of  the  arc  without  making 
use  of  the  radiation  from  it.  He  allowed  small  parts  of 
the  heated  anode  to  fall  into  a  calorimeter  and  measured 
the  heat  which  they  gave  out.  Assuming  that  the  specific 
heat  of  the  carbon  is  the  same  at  the  higher  temperatures 
as  it  is  at  the  lower,  the  temperature  of  the  arc  was  com- 
puted from  this  amount  of  heat.  This  assumption  is  as 
reasonable  as  any  made  in  attempting  to  solve  this  problem, 
but  the  experimental  difficulties  of  this  method  are  very 
great.  When  one  remembers  that  only  small  pieces  of 
the  carbon  can  be  used  and  that  only  one  surface  of  these 
can  have  the  temperature  of  the  anode,  it  is  surprising 
that  Violle's  results  were  as  similar  to  those  found  by  more 
recent  methods  as  they  are.  By  this  method  he  com- 
puted the  temperature  of  the  anode  crater  to  be  3600°  C. 

During  the  last  few  years  there  has  been  a  great  advance 
in  our  knowledge  of  the  radiation  from  " black  bodies." 
Such  a  body  would  be  one  which  absorbs  completely  radi- 
ations of  all  lengths  which  impinge  upon  it.  There  are  four 
equations  concerning  the  radiation  from  such  a  body 
which  have  been  deduced  from  theoretical  considerations: 
the  Stefan-Boltzmann  law,  i.e.,  E  =  cT*,  where  E  is  the 
total  radiation  from  the  black  body,  T  its  absolute  tem- 
perature and  c  a  constant;  Wien's  displacement  law,  i.e., 
\mT  =  const.,  where  \m  is  the  wave  length  having  the 
maximum  amount  of  energy;  Wien's  law  for  the  distri- 
bution of  energy  in  the  spectrum  from  a  black  body,  i.e., 

1  C.  R.,  115,  1273;  1892.  Journ.  de  Phys.,  (3),  2,  545;  1893. 


ARC   IN  AIR   BETWEEN   CARBON   ELECTRODES         43 

_   °2 

J=  c{K~5  e  X2\  where  /  is  the  amount  of  energy  of  any 
given  wave  length,  X  the  wave  length,  and  Ci  and  c2  con- 
stants; and  Planck's  modification  of  Wien's  law,  i.e., 

\~5 
J=  d  -         — .     This  last  has  been  found  to  hold  through 

6*-I 

a  more  extended  range  of  temperature  than  that  of  Wien's, 
but  for  wave  lengths  in  the  visible  spectrum  Wien's  law 
applies  with  sufficient  precision. 

Although  these  equations  have  been  proven  only  for 
ideal  black  bodies,  carbon  comes  sufficiently  near  to  being 
such  a  body  to  enable  us  to  make  use  of  them  in  getting 
an  approximate  value  for  the  temperature  of  the  arc. 
The  first  of  the  equations  was  used  by  Fery1  and  the  value 
which  he  gave  to  the  temperature  was  3490°  C. 

Lummer  and  Pringsheim  used  the  second  formula. 
They  were  led  to  believe  that  the  radiations  from  the  car- 
bon of  the  arc  were  intermediate  between  those  from 
platinum  and  those  from  a  black  body.  From  this  they 
computed  the  temperature  of  the  arc  to  lie  between  3750 
and  4200  degrees  absolute  temperature.  Very2  applying 
this  same  method  to  data  given  by  Abey  and  Festing3 
gave  the  temperature  of  the  arc  as  between  3600  and  4000 
degrees  absolute. 

Wanner,  using  the  third  formula,  found  the  temperature 
to  vary  from  3700  to  3900  degrees  absolute,  depending 
on  the  kind  of  carbon  used.  Fery  using  the  same  method 
gave  a  much  higher  value.  Waidner  and  Burgess4  using 

1  C.  R.,  134,  977  and  1201;  1902. 

2  Astrophys.  Journ.,  10,  209;  1899. 

3  Proc.  Roy.  Soc.,  35,  334;  1883. 

4  Phys.  Rev.,  19,  241;  1904,     Bull,  of  Bureau  of  Standards,  1, 113;  1904. 


44 


THE  ELECTRIC  ARC 


three  different  kinds  of  pyrometers  in  connection  with 
the  same  formula  found  values  varying  from  3860  to  3720 
degrees  absolute.  A  comparison  of  these  results  is  given 
in  the  following  table,  which  is  taken  from  the  article  by 
Waidner  and  Burgess. 


Observer. 

Absolute  tem- 
perature of 
the  arc. 

Method. 

Le  Chatelier.  .  . 

degrees 
4370 

Photometric  ;  intensity  of  red  light. 

Violle  
Wilson  and  Gray  j 

Wanner                            j 

3870 
3600        J 

Calorimetric  ;  specific  heat  of  carbon. 
Total  radiation  of  copper  oxide,  empirical  rela- 
tion for. 
(Varying  with  carbon  used.)     Photometric  in 

Very                               { 

Between 

terms  of  Wien  s  law. 
Wave  length  of  maximum  energy,  Wien's  dis- 

Lummer and 
Pringsheim  

Fery  j 

3600  and  4000 
Between 
3750  and  4200 
03760 

placement  law;  \mT  =  C. 
Wave  length  of  maximum  energy,  Wien's  dis- 
placement law;  \mT  =  C. 
Total  Radiation;   Stefan-Boltzmann  law. 

Waidner  and  Burgess  .  ] 

04150 
3690 
63680 
3720 

Photometric;  Wien's  law. 
Holborn-Kurlbaum  pyrometer. 
Wanner  pyrometer.                           Wien's  law. 
Le  Chatelier  pyrometer. 

a  Black  body  temperature. 

b  Pure  graphite  gives  a  temperature  not  over  50  degrees  higher. 

They  say  concerning  this:  "From  this  table  it  will  be 
seen  that  the  photometric  methods  based  on  the  extrap- 
olation of  Wien's  equation  show  that  the  '  black  body 
temperature  of  the  arc'  (pure  graphite)  is  at  least  3750 
degrees  absolute,  so  that  its  true  temperature  must  be 
higher  than  this;  it  is  not  possible  to  state  how  much,  in 
the  absence  of  more  definite  knowledge  concerning  the  de- 
parture of  carbon  from  black  body  radiation.  In  the  light 
of  the  best  evidence  that  is  at  present  available  it  would 
seem  that  the  true  temperature  of  the  hottest  part  of 
the  positive  carbon  is  between  3900  and  4000  degrees 
absolute." 

Variation  in  the  Temperature  of  the  Arc.  —  There  has 
been  a  difference  of  opinion  among  different  experimenters 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES        45 

as  to  whether  the  temperature  of  the  carbon  terminals  is 
the  same  under  all  conditions.  Some  have  believed  that 
it  is  the  temperature  at  which  carbon  vaporizes  and 
consequently  is  always  the  same.  Others  have  believed 
that  they  have  found  changes  in  the  temperature.  Wilson1 
examined  the  luminosity  of  the  anode  with  different  pres- 
sures of  the  surrounding  gas  and  found  that  with  higher 
pressures  it  was  less  luminous.  At  20  atmospheres  it  had 
fallen  to  a  dull  red.  He  concluded  that  the  temperature 
of  the  crater  depended  on  how  much  it  was  cooled  by  the 
surrounding  gas. 

Later  experiments  by  Wilson  and  Fitzgerald2  led  them 
to  believe  that  this  decrease  in  the  luminosity  was  due  to 
the  formation  of  NO2,  which  became  so  abundant  at  the 
higher  temperatures  as  to  decrease  the  amount  of  light 
appreciably.  They  were,  therefore,  unable  to  tell  whether 
the  temperature  of  the  carbons  decreased  or  not. 

Waidner  and  Burgess  in  the  course  of  their  work  varied 
the  current  from  15  to  30  amperes,  and  concluded  that 
the  temperature  of  the  positive  anode  increased  about 
70  degrees. 

On  the  other  hand  Reich3  using  a  Wanner  pyrometer 
found  the  temperature  of  the  cathode  to  be  3140  degrees 
absolute,  with  currents  varying  from  3  to  12  amperes. 
He  found  the  temperature  of  the  anode  to  be  3700  degrees 
absolute,  which  was  also  independent  of  the  current.  He 
believed  that  the  change  observed  by  Waidner  and  Burgess 
may  have  been  due  to  the  increased  brilliancy  of  the  gases 
in  the  arc  with  larger  currents.  He  found,  however,  that 

1  Proc.  Roy.  Soc.,  58,  174;  1895. 

2  Proc.  Roy.  Soc..  60,  377;  1897. 

3  Phys.  ZS.,  7,  735  1906. 


46  THE   ELECTRIC   ARC 

sudden  changes  in  the  current  produced  a  decided  effect 
on  the  cathode.  A  sudden  decrease  in  the  current  caused 
the  cathode  to  become  dimmer,  but  it  quickly  became  hot 
again,  although  smaller  in  extent. 

An  attempt  was  made  by  myself1  to  find  the  temperature 
of  the  vapor  of  a  carbon  arc  in  a  vacuum,  but  nothing 
more  definite  was  determined  than  that  the  temperature 
with  as  low  a  pressure  as  0.5  mm.  was  high  enough  to 
melt  a  fine  platinum  wire.2 

Effect  Produced  by  Cooling  the  Electrodes.  —  There  has 
been  much  discussion  among  experimenters  as  to  whether 
higher  voltages  are  required  with  cooled  electrodes  or  with 
those  not  cooled.  Since  this  has  some  bearing  on  the 
theory  of  the  arc  it  is  a  matter  of  importance.  We  may, 
however,  pass  over  the  work  of  the  earlier  experimenters, 
since  they  seem  to  have  worked  without  due  consideration 
of  the  conditions.  For  example  de  la  Rive3  attempted  to 
heat  the  arc  by  placing  an  alcohol  lamp  under  it.  There 
would  be  three  results  produced  by  this  experiment  other 
than  the  one  which  he  had  in  mind.  First,  the  flame 
would  probably  cool  the  carbons  of  the  arc  instead  of 
heating  them.  Secondly,  the  flame  would  blow  the  arc 
out  of  its  original  shape,  and  thus  cause  a  greater  drop  in 
potential  through  it.  Lastly,  the  gases  of  the  flame  would 
change  the  character  of  the  arc  and  this  might  have  a 
very  appreciable  effect  on  the  voltage. 

Again  Lecher 4  cooled  one  of  the  electrodes  of  the  arc  by 
immersing  it  in  a  mercury  bath  which  was  in  turn  kept 

1  Phys.  Rev.,  19,  123;  1904. 

2  The  temperature  of  the  mercury  arc  will  be  considered  in  connection 
with  the  other  experiments  on  that  arc. 

3  Archive  de  1'Electricite,  i,  262;  1841. 

4  Wien.  Sitzungsber.,  95,  2  A,  992;  1887. 


ARC   IN  AIR  BETWEEN   CARBON  ELECTRODES        47 

cool  by  running  water,  and  concluded  that  cooling  the 
electrode  decreased  the  amount  of  voltage  required.  It 
has  somewhat  recently  been  shown  by  myself1  that  this 
decrease  was  caused  by  vapor  from  the  mercury  passing 
into  the  arc  and  that  when  this  did  not  occur  the  voltage 
increased.  Indeed  several  experiments  which  were  sup- 
posed to  show  that  cooling  the  electrode  lowered  the  volt- 
age were  repeated  by  myself,  and  when  proper  care  was 
taken  it  was  found  that  in  every  case  cooling  the  electrodes 
raised  the  required  voltage. 

This  is  also  what  one  would  expect  from  a  consideration 
of  the  phenomena  bearing  indirectly  on  the  subject.  For 
example,  if  the  terminals  of  the  arc  are  separated  for  some 
distance  when  it  is  first  started,  the  arc  is  more  apt  to  go 
out  than  it  is,  if  the  terminals  are  allowed  to  become  hot 
before  being  separated.  If  then  a  longer  arc  can  be 
maintained  when  the  carbons  are  hot,  one  would  conclude 
that  heating  the  terminals  allows  the  current  to  flow 
with  a  smaller  potential  difference.  With  an  alternating- 
current  arc  it  requires  a  higher  voltage  for  a  given  current 
when  the  current  is  increasing  than  when  it  is  decreasing. 
When  it  is  increasing,  the  arc  has  been  cooled  and  has  not 
yet  attained  its  maximum  temperature.  When  it  is  de- 
creasing, it  has  been  hot  and  is  cooling,  so  that  with  the 
same  current  the  electrodes  are  cooler  in  the  first  place 
than  in  the  second. 

Again  it  is  much  more  difficult  to  maintain  an  arc  in 
hydrogen  than  in  air,  and  this  has  generally  been  ex- 
plained as  being  due  to  the  fact  that  hydrogen  cools  the 
electrodes  more  rapidly  than  air,  as  if  cooling  the  electrodes 
made  necessary  a  greater  potential  difference. 

1  Phys.  Rev.,  30,  315;  1910. 


48  THE  ELECTRIC   ARC 

Probably  the  most  satisfactory  method  of  showing  the 
effect  which  cooling  the  electrode  has,  is  to  pass  an  arc  be- 
tween copper  or  carbon  tubes  and  to  observe  the  voltage 
first  when  the  tubes  are  hot  and  second  when  they  are 
somewhat  cooled  by  passing  water  through  the  interior  of 
the  tubes.  This  method  has  been  used  by  Tommasi,1 
Schultze,2  Malcolm  and  Simon,3  and  myself4  and  all  have 
found  that  with  cooled  electrodes  higher  voltages  are  re- 
quired.5 

The  changes  in  the  anode  and  cathode  drops  were  also 
examined  by  myself,  and  it  was  found  that  the  greater  part 
of  the  change  in  voltage  was  due  to  a  change  in  the  anode 
drop.  The  change  in  the  different  parts  of  the  arc  is 
roughly  proportional  to  the  potential  difference  existing  in 
those  parts  before  the  cathode  is  cooled. 

Size  of  the  Anode  Crater.  —  It  is  well  known  that  the 
size  of  the  anode  crater  increases  as  the  current  is  in- 
creased, but  there  seems  to  be  no  agreement  as  to  exactly 
how  large  it  is,  nor  what  the  exact  relation  is  between  its 
area  and  the  current.  Andrews6  found  the  area  of  the 
crater  to  be  directly  proportional  to  the  current.  Mrs. 
Ayrton,  using  cored  carbons,  found  it  to  be  a  linear  func- 
tion of  the  current,  but  not  quite  proportional  to  it.7  She 
states  that  with  a  current  of  4  amperes  the  diameter  was 

1  C.  R.,  93,  716;  1881. 

2  Ann.  d.  Phys.,  12,  837;  1903. 

3  Phys.  ZS.,  8,  478;  1907- 

4  Phys.  Rev.,  30,  310;  1910. 

6  Other  experiments  were  performed  by  the  following: 

Cross  and  Shepard,  Proc.  Amer.  Acad.  Sc.,  22,  227;   1885. 

Mitkiewicz,  Beib.,  29,  739;   1904. 

Stark  and  Cassuto,  Phys.  ZS.,  5,  265;   1904. 

6  Journ.  Tel.  Eng.,  9,  201;  1880. 

7  Mrs.  Ayrton's  "  Electric  Arc,"  p.  151. 


ARC  IN  AIR  BETWEEN  CARBON  ELECTRODES        49 

3.1  mm.  and  with  20  amperes  6.4  mm.  She  also  found 
the  diameter  to  increase  slightly  as  the  length  of  the  arc 
was  increased. 

Granqvist 1  gives  the  following  formula  for  the  crater  with 
solid  carbons,  r  =  0.043  +  0.008  /,  where  r  is  the  radius  in 
centimeters  and  /  is  the  current  in  amperes.  As  will  be 
noticed,  these  results  are  very  different  from  those  given 
by  Mrs.  Ayrton  for  cored  carbons. 

Reich2  found  that  the  bright  spot  on  the  cathode,  which 
he  calls  the  negative  crater,  was  larger,  the  shorter  the  arc. 
With  an  arc  9  mm.  long  the  following  formula  applied: 
r  =  o.oi  +  0.009  /  centimeters. 

Enclosed  Arc.  —  With  the  common  arc  in  air  each  of 
the  carbons  is  consumed  at  the  rate  of  about  one  inch  per 
hour.  This  loss  is  principally  due  to  oxidation  of  the 
carbon.  The  simplest  means  of  obviating  this  is  to  place 
the  arc  in  an  air-tight  globe,  but  it  has  been  found  that  if 
it  is  completely  air-tight,  carbon  vapors  and  hydrocarbon 
compounds  diffuse  to  the  side  of  the  globe  making  it  more 
or  less  opaque.  It  was  found,  however,  by  Marks3  that  if 
the  arc  is  one  with  small  current  and  sufficient  length,  so 
as  to  require  a  comparatively  high  voltage,  it  is  possible 
to  admit  air  in  such  small  amounts  that  the  rate  of  com- 
bustion of  the  carbons  is  greatly  reduced,  while  there  is 
still  enough  air  to  oxidize  the  carbon  vapors. 

With  the  lamp  first  made  by  Marks  there  was  a  valve 
which  allowed  a  small  amount  of  air  to  enter.  With  im- 
proved carbons  this  has  not  been  found  necessary.  There 
is  usually  some  chance  for  the  leakage  of  air  in  the  space 

1  Phys.  ZS.,  7,  79;  1906. 

2  Phys.  ZS.,  7,  73;  1906. 

3  Lond.  Elec.,  31,  502;  1893,  and  38,  615;  1897. 


50  THE   ELECTRIC   ARC 

between  the  movable  carbon  and  the  insulator  about  it, 
and  this  is  sufficient  to  allow  the  necessary  amount  of  air 
to  enter. 

The  ends  of  the  carbons  with  the  enclosed  arc  remain 
more  nearly  flat,  the  crater  of  the  anode  being  less  de- 
pressed, and  the  cathode  point  being  less  prominent.  The 
resulting  distribution  of  light  is  somewhat  different  from 
that  given  by  the  open-carbon  arc. 

The  great  advantage  of  this  form  of  arc  is  that  the  car- 
bons do  not  need  to  be  renewed  nearly  as  often  as  with 
the  open  arc.  This  is  more  of  an  advantage  in  this  country 
where  the  cost  of  labor  is  higher  than  in  Europe.  As  a 
result  it  has  been  used  very  largely  here,  and  very  little  in 
places  where  labor  is  cheap. 

Characteristic  curves  of  these  arcs  do  not  seem  to  have 
been  published,  but  it  may  be  said  that  in  general  the  volt- 
age of  an  enclosed  arc  is  higher  than  that  for  an  open  arc 
of  the  same  length  and  current  between  the  same  carbons. 
As  an  example  of  this  it  was  found  that  the  voltage  of 
the  arc  in  a  commercial  lamp  using  6.5  amperes  and 
having  a  length  of  8  mm.  was  80  volts. 

Miscellaneous.  —  There  are  a  few  more  or  less  isolated 
facts  concerning  the  carbon  arc  which  should  be  men- 
tioned before  passing  to  other  topics.  Such,  for  example, 
is  the  fact  that  an  arc  is  deflected  when  in  a  magnetic 
field.  The  first  mention  of  this  seems  to  have  been  made 
by  Davy  in  182 11  and  Walker2  states  that  the  arc  will 
rotate  if  one  of  the  electrodes  is  a  steel  magnet.  Blondel3 
took  photographs  of  the  alternating-current  arc  in  a  mag- 

1  Phil.  Trans.,  p.  428,  1821. 

2  Pogg.  Ann.,  54,  514;  1841. 

3  Lum.  Elec.,  43,  54;  1892. 


ARC   IN  AIR  BETWEEN  CARBON  ELECTRODES         51 

netic  field  and  found  that  it  was  deflected  alternately,  as 
if  it  was  wire  which  was  carrying  current. 

In  1878  Wilde1  showed  that  the  reason  an  arc  between 
two  parallel  carbons  travels  away  from  the  ends  at  which 
the  current  enters  the  carbons  is  that  the  magnetic  action 
cf  the  current  upon  itself  forces  it  in  this  direction. 
Somewhat  recently  Morris 2  examined,  by  means  of  an  oscil- 
lograph, the  current  through  an  arc  just  before  it  was 
broken  by  being  deflected  by  a  magnet  and  showed  that 
it  was  a  pulsating  current.  This  accounts  for  the  shriek 
which  the  arc  gives  when  it  is  thus  extinguished.3 

While  making  photometric  measurements  with  rotating 
sectors,  Trotter4  discovered  that  there  is  a  bright  spot 
near  the  middle  of  the  crater  which  rotates  with  frequen- 
cies varying  from  50  to  450  per  second,  the  most  common 
being  about  100  per  second.  This  was  most  noticeable 
with  short  humming  arcs.  The  direction  of  rotation 
varied  without  any  known  cause. 

Dewar5  showed  that  the  vapors  of  the  arc  exert  a  pres- 
sure on  the  electrodes,  that  on  the  anode  being  the  greater. 
This  has  been  verified  by  Cheneveau.6 

1  Nature,  19,  152;  1878. 

2  Lond.  Elec.,  59,  707;  1907. 

3  Other  experiments  with  an  arc  in  a  magnetic  field  have  been  performed 
by  the  following: 

Cassellman,  Pogg.  Ann.,  63,  589;  1844. 

De  la  Rive,  Phil.  Trans.,  part  i,  37;   1847. 

Quet,  C.  R.,  34,  805;   1821. 

Joubert,  C.  R.,  91,  161;   1880. 

Martiny,  Dissertation  Rostock  and  Ber.  d.  Phys.  Ges.,  2,  199;   1904. 

Child,  Phys.  Rev.,  20,  100;   1905,  and  24,  498;   1907. 

4  Lond.  Elec.,  33,  297;  1894. 

5  Chem.  News,  45,  37;  1882.     Proc.  Roy.  Soc.,  33,  262;  1882. 

6  Eel.  Elec.,  20,  402;  1899. 


52  THE  ELECTRIC  ARC 

The  current  between  a  hot  carbon  used  as  cathode  and 
a  cooler  one  used  as  anode  with  different  temperatures  and 
different  potential  differences  has  been  examined  by  Pollock 
and  Ranchaud.1  They  studied  this  with  especial  reference 
to  the  conditions  under  which  the  current  changes  from  a 
small,  non-luminous  discharge  to  the  arc.  The  hot  carbon 
was  heated  by  passing  an  electric  current  through  it,  and  its 
temperature  was  determined  by  a  Holborn-Kurlbaum  opti- 
cal pyrometer.  The  anode  became  heated  somewhat  by 
the  radiation  from  the  cathode  and  its  temperature  was 
determined  by  a  thermo junction. 


IjO'C 

VOLTS  BETWEEN  CARBONS 

FIG.  13. 

Some  of  their  results  are  given  in  Fig.  13.  The  first 
number  above  each  curve  gives  the  temperature  of  the 
cathode  and  the  second  one  that  of  the  anode.  The 
dotted  parts  of  the  curve  are  extrapolated.  The  crosses 
"x"  indicate  the  points  at  which  the  discharge  became  an 
arc. 

1  Phil.  Mag.,  (6),  17,  366;  1909. 


CHAPTER   III. 

ARC  IN  AIR  BETWEEN  OTHER  SUBSTANCES  THAN  CARBON. 

So  far  we  have  considered  only  arcs  between  terminals 
of  nearly  pure  carbon.  As  has  been  stated  it  is  possible  to 
use  for  terminals  many  other  substances.  Attempts  were 
made  in  the  early  part  of  the  last  century  either  to  use 
a  metal  or  to  add  some  substance  to  the  carbon  which 
would  increase  the  efficiency  of  the  arc  for  giving  light. 
These  attempts  did  not  at  the  time  meet  with  success. 
They  led  rather  to  the  belief  that  the  substance  which 
could  be  raised  to  the  highest  temperature  without  being 
melted  was  the  most  efficient,  and  since  carbon  can  be 
raised  to  a  higher  temperature  than  any  other  material 
which  is  commercially  feasible,  it  was  believed  to  be  the 
best  for  electrodes. 

But  the  discoveries  of  Auer  and  Nernst  showed  that 
there  are  materials  which  have  an  emissive  power  more  or 
less  selective  and  that  an  ideal  black  body  is  not  neces- 
sarily the  best  for  emitting  light.  It,  therefore,  became 
evident  that  there  might  be  some  better  substance  which 
could  be  used  for  the  electrodes  of  the  arc.  Several  of 
those  which  have  since  been  tried  have  met  with  a  large 
degree  of  success.  There  are  now  three  types  of  arcs 
which  embody  some  improvement  over  the  carbon  arc. 
These  are  arcs  having  electrodes  which  are  principally  car- 
bon, but  have  also  a  mixture  of  other  substances,  such  as 
the  " flaming"  arcs;  arcs  having  an  oxide  for  one  of  the 

S3 


54  THE  ELECTRIC  ARC 

electrodes,  of  which  the  magnetite  arc  is  the  best  known; 
and  arcs  between  metals,  of  which  the  mercury  arc  in  a 
vacuum  is  the  only  commercial  example. 

All  of  these  arcs  require  a  lower  voltage  for  the  same 
current  and  length  than  the  carbon  arc,  and  they  all  give 
more  light  for  the  same  amount  of  energy.  It  is  also  true 
that  each  has  some  disadvantage.  Many  compounds 
which  might  be  introduced  into  the  arc  give  fumes  which 
make  them  disagreeable  in  an  enclosed  room,  and  some 
blacken  any  globe  which  may  surround  the  arc.  Many 
give  colors  which  are  better  suited  for  advertising  purposes 
than  for  common  use.  Some  combinations  of  salts  give 
trouble  either  with  regulating  the  lamp,  or  with  starting 
the  arc  after  it  has  been  extinguished. 

Unfortunately  investigation  of  these  arcs  must  be  en- 
tirely empirical,  for  we  know  nothing  of  the  laws  of  radi- 
ation from  mineral  vapors  at  high  temperatures,  nor  of  the 
laws  governing  the  relation  between  electrical  excitation 
of  an  atom  and  its  emission  of  light.  We  can  not  reason 
out  in  advance  the  amount  of  light  to  be  expected  from  a 
given  substance.  An  analysis  of  the  spectrum  of  differ- 
ent vapors  does  not  always  help  us.  The  spectrum  of 
calcium  fluoride,  for  example,  has  no  resemblance  to  that 
of  other  salts  of  calcium  and  is  more  brilliant. 

Flaming  Arc.  —  The  general  appearance  of  the  first  of 
these  types,  namely,  those  whose  electrodes  are  carbon 
with  certain  salts  mixed  with  them,  is  quite  different  from 
that  of  the  arc  between  pure  carbons.  This  is  indicated  by 
Fig.  14,  which  is  reproduced  from  a  photograph  of  a  ''flam- 
ing arc/'  as  this  class  of  arcs  is  called.  This  arc  is  very 
much  longer  than  the  older  form,  and  the  greater  part  of 
the  light  comes  from  the  vapor  instead  of  from  the  carbon. 


ARC   IN  AIR   BETWEEN   OTHER   SUBSTANCES 


55 


The  first  mention  which  I  have  found  of  the  arc  be- 
tween carbons  in  which  other  substances  were  mixed  is 
that  in  an  article  by  Casselmann1  who  tried  the  effect  of 


FIG.  14. 

introducing  different  salts  into  the  arc  and  found  that 
they  allowed  longer  arcs  with  the  same  number  of  cells. 
He  found  that  strontium  nitrate,  copper  nitrate,  and  zinc 
chloride  were  especially  helpful  in  producing  luminosity.2 

1  Pogg.  Ann.,  63,  576;  1844. 

2  Other  investigations  were  made  by  the  following: 

Archereaus,  C.  R.,  84,  137;   1877. 

Carre,  C.  R.,  84,  346;   1877. 

Luggin,  Centralbl.  f.  Elektrot,  10,  567;   1888.    ' 


56  THE   ELECTRIC   ARC 

The  first  commercial  success  in  this  direction  was 
made  by  Bremen  who  discovered  the  advantage  of  using 
calcium  fluoride.  This  is  the  basis  of  nearly  all  the  com- 
binations of  salts  used  for  flaming  arcs.  Other  salts  are 
added  to  a  greater  or  less  extent  to  modify  the  kind  of 
light,  or  to  avoid  some  of  the  disadvantages  mentioned 
above.  Thus  calcium  phosphate  is  often  added,  especially 
for  direct-current  arcs.  According  to  Mahlke1  cerium 
chloride  forms  two-thirds  of  the  salts  used  for  white  flaming 
arcs,  the  other  third  being  chiefly  calcium  salts. 

The  carbon  for  these  lamps  consists  of  an  outer  cylinder 
made  of  hard  carbon  and  an  inner  core  made  of  a  mixture 
of  carbon  and  the  salts  to  be  used.  The  outer  cylinder 
protects  the  salts  from  too  rapid  consumption  and  gives 
the  necessary  conductivity  to  the  electrode.  The  inner 
core  is  made  of  a  finely  divided  carbon,  usually  lamp- 
black, mixed  with  the  salt,  which  must  be  in  the  form  of 
a  powder.  If  the  salt  is  not  thoroughly  mixed  with  the 
carbon,  they  will  produce  miniature  explosions  and  uneven 
burning  of  the  arc. 

According  to  Mahlke  the  core  consists  of  40  per  cent  of 
lampblack  and  60  per  cent  of  metallic  salt.  There  are, 
however,  few  of  the  flaming-arc  carbons  now  on  the  market 
which  have  as  high  a  percentage  of  salt  as  this. 

The  resistance  of  these  electrodes  is  higher  than  that 
of  solid  carbons,  and  if  they  are  long,  much  energy  is 
wasted  in  forcing  the  current  through  them.  To  remedy 
this,  wires  are  usually  run  through  the  length  of  the  elec- 
trodes to  serve  as  conductors.  These  wires  vary  from  one- 
half  to  three-fourths  of  a  millimeter  in  diameter.  Zinc, 
brass  and  tin  have  been  used  for  this  purpose. 

1  Elec.  World,  57,  675;  1911. 


ARC   IN  AIR   BETWEEN   OTHER   SUBSTANCES  57 

The  great  advantage  of  these  arcs  is  that  they  give  much 
more  light  for  the  power  consumed  than  carbon  arcs. 
They  also  have  two  disadvantages.  One  of  these  is  the 
color  of  the  light  given.  With  the  " white"  flaming-arc 
carbons  now  on  the  market  this  difficulty  has  been  largely 
obviated,  the  light  from  these  being  nearly  the  same  as; 
that  from  common  carbons.  However,  what  is  thus 
gained  in  color  is  lost  to  some  extent  in  efficiency,  the 
watts  per  candle  for  the  " white"  flaming  arc  being  some- 
what greater  than  those  for  the  " yellow"  flaming  arc. 

The  chief  disadvantage  of  the  flaming  arc  is  that  the 
carbons  are  more  rapidly  consumed  than  those  of  the  com- 
mon carbon  arc,  and  very  much  more  rapidly  than  those 
of  the  enclosed  arc,  and  require  more  frequent  renewal. 
For  this  reason  the  flaming  arc  has  not  been  widely  used 
in  this  country  where  the  cost  of  labor  is  high.  In  Europe 
they  have  been  very  extensively  used. 

Considerable  progress  is,  however,  being  made  in  obviat- 
ing this  difficulty  by  special  forms  of  lamps.  In  many  of 
these  the  air  is  partially  excluded,  as  in  the  enclosed  arcs, 
and  ventilating  flues  which  keep  the  solid  products  of  com- 
bustion from  being  deposited  on  the  surrounding  globe  are 
provided.  The  life  of  the  electrodes  has  by  this  means 
been  increased  to  80  or  even  100  hours. 

The  life  of  the  electrodes  can  be  increased  by  making 
either  the  electrodes  longer  or  their  diameters  greater.  In- 
crease in  length,  however,  leads  to  an  unsightly  and  clumsy 
lamp,  while  increase  in  diameter  leads  to  unsteadiness. 
Increased  life  can  also  be  attained  by  using  carbons  which 
approach  in  composition  more  nearly  to  the  common  car- 
bon, but  such  increase  leads  to  a  decided  loss  in  efficiency. 

The  potential  difference  needed  to  maintain  the  flaming 


THE  ELECTRIC  ARC 


arc  is  much  less  than  that  needed  for  carbon  arcs.  Scarcely 
any  measurements  have  been  published  regarding  this, 
but  a  few  observations  have  been  recently  made  by  my- 


70 


60 


50 


040 


30 


20 


10 


16 


20 


4         8         12 

LENGTH  IN  MM. 
FIG.  15. 

self  and  are  given  in  Fig.  15.  With  different  settings  for 
length  the  readings  of  the  voltmeter  varied  by  one  or  two 
volts,  but  by  taking  several  observations  an  average  was 
found  which  represents  closely  the  correct  value. 

Curve  a  in  Fig.  15  represents  the  voltages  for  different 


ARC  IN  AIR  BETWEEN  OTHER   SUBSTANCES  59 

lengths  with  what  is  known  as  the  "white"  flaming  arc. 
The  current  was  kept  constant  at  10  amperes.  For  com- 
parison the  corresponding  curve  for  the  open  carbon  arc  as 
plotted  from  Mrs.  Ayrton's  equation  is  given  in  curve  d. 
The  great  difference  between  the  two  forms  of  arc  is  very 
evident. 

The  data  plotted  in  curve  a  were  taken  with  the  open 
flaming  arc  having  the  carbons  vertical,  the  positive  one 
being  below.  In  general  the  flaming  arc  is  enclosed  in 
some  kind  of  a  globe  and  usually  with  some  arrangement 
to  produce  a  draft  which  will  keep  the  ash  from  settling  on 
the  globe.  This  curve,  therefore,  does  not  give  the  exact 
voltage  which  would  be  needed  when  running  under  com- 
mercial conditions.  It  does,  ho'wever,  give  an  approxi- 
mate idea  of  such  voltage. 

Observations  were  also  made  of  the  voltage  with  the 
flaming  arc  enclosed  in  a  globe  which  was  very  nearly  air- 
tight. The  data  thus  taken  are  plotted  in  curve  b. 

Observations  were  made  with  carbons  which  were  pur- 
chased from  several  different  dealers  and  were  supposed  to 
be  different  kinds  of  carbons.  With  one  exception  they 
showed  but  slight  differences  as  far  as  the  potential  differ- 
ence at  the  terminals  was  concerned,  so  that  the  curves 
given  in  Fig.  15  would  apply  fairly  well  to  nearly  all  of  the 
carbons.  The  one  exception  gave  higher  voltages  with  the" 
longer  arcs.  For  example,  with  an  arc  22  mm.  long  the 
voltage  was  51  instead  of  47  volts. 

The  voltages  required  for  the  "yellow"  flaming  arc  are 
slightly  less  than  those  of  the  white  arc.  Such  an  arc  is 
represented  by  the  curve  c. 

In  Fig.  1 6  there  is  given  a  curve  showing  the  voltages 
with  different  currents,  the  length  being  constant  at  10  mm. 


6o 


THE  ELECTRIC  ARC 


This  curve  represents  the  voltages  with  the  white  arc. 
Those  with  the  yellow  arc  were  only  slightly  less  than 
these.  This  curve  differs  from  those  given  by  Mrs.  Ayrton 
for  the  carbon  arc  in  that  it  shows  an  increase  with  the 
larger  currents.  This  was  apparently  due  to  the  tendency 
of  the  arc  with  the  larger  currents  to  flare  out  to  one  side. 
It  was  very  difficult  with  the  currents  of  more  than  25 
amperes  to  get  a  steady  condition  and  different  readings 


40 


30 


20 


1 6  24 

CURRENT 

FIG.  i 6. 


32 


40 

AMPERES 


varied  by  3  or  4  volts.  But  the  voltage  with  the  large  cur- 
rents appeared  even  with  the  most  steady  conditions  to  be 
greater  than  those  required  for  20  amperes. 

The  small  voltage  required  for  the  flaming  arc  is  largely 
due  to  the  small  drop  in  potential  at  the  anode.  The  de- 
crease in  the  anode  drop  caused  by  putting  salts  in  the  arc 
was  shown  several  years  ago  by  Luggin1  who  found  that 
sprinkling  the  carbons  with  soda  diminished  the  anode  drop 
to  less  than  one-half  of  its  former  value. 

In  the  examination  of  flaming  arcs  made  by  myself  it 

1  Centralbl.  f.  Elektrot,  10,  567;  1888. 


ARC  IN  AIR  BETWEEN  OTHER  SUBSTANCES  6l 

was  found  that  the  drop  between  the  anode  and  carbon 
pencil  i  mm.  in  diameter  placed  as  close  to  the  anode  as 
possible  without  touching  it  was  12  volts.  The  drop  be- 
tween such  a  pencil  and  the  cathode  was  8.5  volts.  These 
observations  were  made  with  open  arcs  i  cm.  long  and 
having  a  current  of  10  amperes.  The  values  were  found 
to  be  nearly  independent  of  the  length  of  arc  or  the  current 
and  were  the  same  for  several  different  makes  of  flaming- 
arc  carbons.  The  anode  drop  with  arcs  of  the  same 
length  and  current  between  solid  carbons  is  35  volts  (p.  14) 
which  is  approximately  three  times  that  for  the  flaming 
arcs,  while  the  cathode  drop  is  nearly  the  same  for  both 
kinds  of  carbons. 

The  electric  force  through  the  arc  can  be  found  ap- 
proximately by  getting  the  rate  of  change  of  the  potential 
difference  between  the  terminals  of  the  arc  with  respect 
to  the  length.  The  data  on  the  preceding  page  show 
that  this  rate  of  change  was  approximately  1.65  volts  per 
millimeter  for  the  open  flaming  arc  when  the  current 
was  10  amperes,  while  with  the  arc  between  solid  car- 
bons the  value  of  this  quantity  is  3.12  volts  per  milli- 
meter. 

Arc  between  Metals.  —  With  the  exception  of  the  arc 
between  mercury  terminals  in  a  vacuum  none  of  the  arcs 
between  metals  have  proven  to  be  of  commercial  value, 
for  the  metals  are  consumed  much  more  rapidly  than 
carbon  and  the  arcs  between  them  sputter  continually  and 
give  much  less  light  than  carbon  arcs.  Many  investiga- 
tions have,  however,  been  made  for  the  purpose  of  learn- 
ing how  such  arcs  behave.  The  earlier  of  these  were  of 
less  value  because  one  can  not  be  sure  whether  the  experi- 
menter was  using  an  arc  or  only  a  spark.  However,  there 


62  THE  ELECTRIC  ARC 

were  a  few  facts  clearly  shown  in  the  early  part  of  the  last 
century.  For  example,  it  was  shown  by  Davy1  that  car- 
bon terminals  give  out  more  light  than  any  of  the  metals. 
It  was  shown  by  Metteucci2  that  the  conductivity  of  the 
arc  between  copper  terminals  was  more  than  that  between 
some  of  the  other  metals. 

Somewhat  later  it  was  shown  by  Edlund3  that  there  was 
no  measurable  conductivity  between  silver  terminals  1/80 
sec.  after  the  arc  had  been  extinguished,  although  with 
carbon  terminals  there  was  a  very  appreciable  amount  of 
conductivity.  It  has  since  been  shown  that  all  arcs  be- 
tween metals  lose  their  conductivity  very  rapidly  after  the 
removal  of  the  impressed  E.M.F.4 

It  is  only  in  recent  years  that  measurements  have  been 
made  on  the  relation  between  potential  difference,  current 
and  length  of  metal  arcs.  These  measurements  show  that 
the  metal  arcs  require  a  much  smaller  voltage  than  the 
carbon  arcs  for  the  same  current  and  length  of  arc  and 
that  the  characteristic  curves  are  quite  similar  to  those  for 
the  carbon  arc,  but  the  fact  which  they  most  clearly  show 
is  that  different  experimenters  working  under  different 
conditions  arrive  at  very  different  results.  This  is  seen 
from  the  following  formulas  which  have  been  given  for  this 
relation  for  the  arc  between  copper  terminals.  In  all  of 
these  E  represents  the  potential  difference  in  volts,  /  the 
current  in  amperes  and  /  the  length  of  the  arc  in  milli- 
meters. 

1  Journ.  Roy.  Inst.,  I,  166;  1802. 

2  C.  R.,  30,  201;  1850. 

3  Pogg.  Ann.,  134,  250;  1868. 

4  See  also  the  following  : 

De  la  Rive,  Phil.  Trans.,  part  2,  31;  1847. 
Arons,  Wied.  Ann.,  57,  197;   1896. 


ARC  IN  AIR  BETWEEN  OTHER   SUBSTANCES  63 

1E  =  26,  for  7  =  5  amperes  and  /  =  2  mm. 

2E  =  23.86+  .67/7. 

3E  =  18.88  +  22.4J-3.9/. 


The  second  of  these  equations  should  probably  not  be 
considered  at  all,  since  other  experimenters  have  shown 
conclusively  that  the  voltage  does  not  increase  with  in- 
creasing current,  but  the  others  are  sufficient  to  show  that 
the  voltage  is  not  only  a  function  of  the  current  and  length 
of  arc,  but  also  of  other  conditions.  Some  of  the  con- 
ditions under  which  these  formulas  were  found  may  be  in- 
dicated by  the  following.  The  third  formula  is  only  true 
for  a  horizontal  arc  of  2  amperes,  the  size  of  the  electrodes 
not  being  given.  The  fourth  is  with  rods  16  mm.  in 
diameter  with  length  of  arc  2  mm.  or  less.  The  fifth  is 
with  rods  three-eighths  inch  in  diameter  with  the  anode 
above,  while  the  sixth  is  for  water-cooled  electrodes  with 
small  currents. 

In  addition  to  these  results  we  have  the  statement  of 
other  experimenters  that  the  curve  for  the  arc  between 
copper  terminals  does  not  follow  any  simple  formula. 

1  Lecher,  Wien.  Sitzungsber.,  95,  2A,  992;  1887. 

2  Von  Lang,  Wied.  Ann.,  31,  391;  1887. 

3  Freedman,  Elec.  Rev.,  37,  253;  1895. 

4  Guy  and  Zebrikoff,  C.  R.,  145,  169;  1907. 

5  Upson,  Phil.  Mag.,  (6),  14,  140;  1908. 

6  Grau  and  Russ,  Phys.  ZS.,  9,  108;  1908. 


64  THE   ELECTRIC   ARC 

Thus,  according  to  Malcolm  and  Simon,1  who  worked  with 
small  currents,  the  product  El  is  not  a  linear  function  of 
/,  as  it  is  in  the  preceding  equations.  They  found  the 
potential  difference  for  an  arc  between  copper  terminals  to 
vary  from  80  volts  for  0.6  ampere  to  58  volts  for  i.i 
amperes,  the  length  in  both  cases  being  4  mm. 

Hagenbach  and  Veillon2  found  it  difficult  to  make  any 
exact  measurements  of  the  copper  arc,  but,  as  far  as  they 
could,  they  determined  its  voltage  both  in  air  and  in  a 
vacuum,  and  in  no  case  did  the  curve  follow  the  Ayr  ton 
formula. 

There  are,  however,  two  facts  upon  which  there  is 
agreement;  first,  that  the  potential  difference  with  arcs 
between  metals  is  in  general  smaller  than  that  between 
carbons,  and  second  that  the  rate  of  increase  with  in- 
creasing length  of  arc  is  greater  than  with  carbon  arcs. 
From  this  it  would  follow  that  the  sum  of  the  anode  and 
cathode  drops  in  the  metal  arcs  is  less  than  in  the  carbon 
arc,  and  that  the  electric  force  is  greater. 

The  difficulty  of  making  accurate  measurements  of  the 
metal  arcs  is  partly  due  to  the  fact  that  there  are  two 
or  more  forms  of  these  arcs,  and  that  under  some  con- 
ditions there  is  a  constant  fluctuation  from  one  form  to 
the  other.  Thus  it  has  been  shown  by  Cady  and  Arnold3 
that  there  are  two  distinct  forms  of  the  arc  between  iron 
terminals  corresponding  somewhat  to  the  quiet  and  hissing 
forms  of  the  carbon  arc.  The  first  stage  occurs  with  small 
currents,  usually  less  than  2  amperes.  The  voltage  is  in 
the  neighborhood  of  75  volts.  The  gas  near  the  anode  is 

1  Phys.  ZS.,  8,  477;  1907. 

2  Phys.  ZS.,  n,  833;  1910. 

3  Amer.  Jour.  Sc.,  (4),  24,  383;  1907. 


ARC  IN  AIR  BETWEEN  OTHER   SUBSTANCES          65 

non-luminous  and  the  arc  is  quiet.  In  passing  to  the 
second  stage  there  is  a  sudden  increase  in  current  and 
decrease  in  potential  difference,  the  gas  near  the  anode 
becoming  luminous  and  the  arc  becoming  noisy. 

Though  there  is  an  apparent  similarity  between  the 
second  stage  of  this  arc  and  the  hissing  arc  with  carbon 
terminals,  the  causes  of  the  two  phenomena  are  not  the 
same.  The  peculiarities  of  the  second  stage  with  the  iron 
arc  are  apparently  due  to  vaporization  of  the  anode. 
The  anode  loses  weight  much  more  rapidly  and  the  spec- 
trum of  the  anode  is  very  plain,  while  with  smaller  cur- 
rents it  was  scarcely  visible.  Moreover  the  effect  was 
shown  to  exist  in  nitrogen  as  well  as  in  air,  so  that  it  can 
not  be  explained  as  being  due  to  the  presence  of  oxygen. 

It  is  claimed  by  Hagenbach  and  Veillon  that  there  are 
six  distinct  forms  of  the  copper  arc,  that  there  are  three 
different  anode  drops  which  may  occur,  and  that  with 
each  of  these  it  is  possible  to  have  two  different  cathode 
drops.  The  same  phenomenon  has  been  found  to  a 
limited  extent  with  other  metals,  although  in  general  the 
first  stage  is  absent  with  metals  having  a  low  melting 
point.1 

Two  attempts  have  been  made  to  find  the  anode  and 
cathode  drops  with  the  arc  between  metals  in  air,  but  it  is 
very  difficult  to  make  accurate  measurements.  The  voltage 
of  such  arcs  under  ordinary  conditions  is  very  variable  and 
the  introduction  of  a  carbon  pencil  causes  it  to  fluctuate 
through  even  greater  ranges.  Moreover,  with  the  intro- 

1  See  also  the  following: 

Cady  and  Vinal,  Amer.  Journ.  Sc.,  (4),  28,  89;    1909. 
Fabry  and  Buisson,  Journ.  d.  Phys.,  (4),  9,  929;    1910. 
Hagenbach,  Physik  ZS.,  12,  1015;    1911. 


66  THE   ELECTRIC   ARC 

duction  of  a  carbon  electrode,  the  vapor  of  the  arc  is  changed 
to  a  certain  extent,  so  that  one  can  not  be  certain  that  the 
anode  drop  is  the  same  as  it  was  before  this  was  intro- 
duced. As  a  result  the  measurements  which  have  been 
made  on  the  anode  and  cathode  drops  can  not  be  con- 
sidered as  more  than  rough  approximations. 

The  measurements  indicate,  however,  that  the  relative 
values  of  the  two  drops  are  quite  different  in  metal  arcs 
from  what  they  are  in  the  carbon  arc.  In  the  latter  the 
anode  drop  is  much  greater  than  the  cathode  drop.  In 
the  former  the  two  are  approximately  the  same,  as  was 
shown  by  Lecher1  for  platinum,  iron,  aluminum  and  copper 
and  by  myself2  for  zinc,  iron  and  copper.  With  graphite 
terminals  in  air  the  anode  and  cathode  drops  are  much 
the  same  as  they  are  with  carbon.3 

With  a  metal  arc  in  a  partial  vacuum  the  measurement 
of  the  potential  within  the  arc  can  be  made  somewhat 
more  accurately.  Banderet4  has  examined  the  anode  and 
cathode  drops  of  the  different  forms  of  the  copper  arc 
when  in  a  vacuum.  As  has  been  stated,  it  is  possible  to 
have  six  different  forms.  In  one  of  these  where  the 
appearance  at  the  anode  is  somewhat  similar  to  that  at 
the  anode  with  the  glow  discharge  in  a  Geissler  tube  he 
found  the  anode  drop  to  be  34  volts.  In  a  form  which 
is  similar  to  the  carbon  arc  the  drop  is  26  volts,  while  in 
an  intermediate  form  it  is  20  volts.  These  measurements 
were  taken  with  a  pressure  of  no  mm.,  a  current  of  5 
amperes,  and  an  arc  length  of  20  mm.  With  all  of  these 

1  Wied.  Ann.,  33,  609;  1888. 

2  Phys.  Rev.,  12,  149;  1901. 

3  Phys.  Rev.,  20,  364;  1905. 

4  Dissertation  Basel,  1912. 


ARC   IN  AIR  BETWEEN  OTHER   SUBSTANCES  67 

the  cathode  drop  is  approximately  13  volts.  Modifica- 
tions of  these  were  also  found  where  the  cathode  drop  is 
slightly  less. 

Arc  between  Oxides.  —  As  has  been  stated,  the  dis- 
coveries of  Auer  and  Nernst  regarding  the  selective 
emissive  power  of  certain  substances  led  to  a  further  investi- 
gation of  the  arc  between  other  substances  than  carbon. 
Among  other  substances  were  oxides  similar  to  those  in 
the  Nernst  lamp.  Rasch  investigated  these  oxides  and 
gives  the  formula  E  =  31.35  +  30/7,  the  length  of  the  arc 
being  i  mm.1  These  oxides  are  non-conductors  at  ordi- 
nary temperatures,  and  an  auxiliary  arc  was  used  to  heat 
them  until  they  became  conductors.  This  arc  has  not 
been  developed  into  a  commercial  form.2 

Measurements  were  made  by  Schultze3  of  arcs  between 
several  oxides  of  metals,  by  placing  the  substance  to  be 
examined  in  a  cup  hollowed  out  of  a  carbon  electrode.  He 
found,  in  general,  that  the  oxide  having  the  lower  melting 
point  requires  the  smaller  E.M.F.  when  used  as  electrode. 
With  very  short  lengths  of  the  arc  he  found  the  voltage  to 
be  independent  of  the  current.  With  greater  length  the 
anode  drop  increased  greatly  with  decreasing  current  and 
the  cathode  drop  increased  little  or  none. 

Magnetite  Arc.  —  The  most  important  of  the  arcs  be- 
tween oxides  is  the  magnetite  arc.4  In  this  the  cathode  is 
magnetite  (Fe3O4)  and  the  anode  is  copper.  Magnetite  is 
used  for  the  cathode  because  it  gives  off  a  vapor  which  is 

1  Elektrot.  ZS.,  22,  55;  1901. 

2  See  also   Elektrot.  ZS.,  22,  256,  293,  and   373;    1901.     Verb.  d.  D. 
Physik.  Ges.,  5,  157;  1903,  and  6,  137;  1904. 

3  Ann.  d.  Phys.,  12,  828;  1903. 

4  Elec.  World,  43,  974;  1904.     Trans.  Intern.  Cong.,  St.  Louis,  2,  721; 
1904. 


68 


THE   ELECTRIC  ARC 


very  luminous  when  in  the  arc,  and  copper  is  used  for  the 
anode  because  it  is  not  rapidly  burnt  away  and  does  not 
need  to  be  renewed  as  often  as  a  carbon  anode.  The  anode 
is  large  and  the  rapid  conduction  of  heat  by  the  copper 
keeps  it  at  a  comparatively  low  temperature.  This  arc  is 
very  efficient  and  the  electrodes  need  little  attention  be- 
cause of  their  slow  consumption. 


200 

160 
Ul 

1^120 
g 

80 

40 


l  r 


2468 
CURRENT  IN  AMPERES 


FIG.  17. 

Characteristic  curves  for  this  arc  are  given  in  Fig.  17. 
The  equation, 

25  +  140  / 

~r 


£=33  + 24.5  * 


which  is  of  the  same  general  form  as  those  given  by  Mrs. 
Ayrton,  agrees  very  closely  with  these  curves. 

Dyott1  gives  characteristic  curves  for  an  arc  having  a 
copper  anode  and  a  cathode  consisting  of  60  per  cent 
magnetite  (Fe3O4),  27  per  cent  titanium  oxide  (TiC^)  and 
13  per  cent  chrome  iron  (FeCr2O4).  His  values  of  the  volt- 

1  Elec.  World,  51,  854;  1908. 


ARC   IN  AIR   BETWEEN   OTHER   SUBSTANCES  69 

ages  for  lengths  greater  than  0.2  inch  are  in  general  greater 
than  those  for  the  magnetite  arc,  while  for  arcs  shorter 
than  this  they  are  less.1 

A  somewhat  similar  arc  is  described  by  Weedon2  in 
which  titanium  carbide  is  used  for  the  cathode  and  copper 
for  the  anode.  The  characteristic  curves  which  he  gives 
for  this  arc  are  nearly  identical  with  those  given  by  Stein- 
metz  for  the  magnetite  arc. 

Arc  between  Electrolytes.  —  As  has  been  stated  it  re- 
quires a  very  high  E.M.F.  to  produce  an  arc  between  a 
metal  and  an  electrolyte,  and  when  produced  it  is  very 
unsteady.  As  far  as  I  have  been  able  to  learn,  no  measure- 
ments of  current  nor  potential  difference  have  been  taken 
with  such  arcs.  About  all  that  has  been  attempted  is  to 
show  that  it  is  possible  to  have  arcs  of  this  kind.  Thus 
Grove3  found  that  water  could  be  made  the  anode  of  an 
arc  and  somewhat  less  easily  the  cathode,  platinum  being 
the  other  terminal.  His  source  of  current  was  500  nitric- 
acid  cells.4 

Arc  between  Unlike  Electrodes.  —  It  was  noticed  by 
Grove  in  i84o5  that  the  current  through  an  arc  is  larger, 
if  it  passes  from  a  metal  which  is  easily  oxidized  to 
platinum  than  if  it  passes  in  the  opposite  direction.  Many 
years  later  it  was  discovered  by  Sahulka  that  with  an 
alternating-current  arc  between  cored  carbon  and  iron 

1  See  also  Ladoff,  Elec.  World,  45,  757;   1905. 

2  Paper  read  at  the  meeting  of  the  Amer.  Chem.  Soc.,  Oct.,  1909. 

3  Phil.  Trans.,  142,  88;  1852. 

4  See  also  the  following: 

Van  der  Willigan,  Pogg.  Ann.,  93,  285;  1854. 
Stark  and  Cassuto,  Phys.  ZS.,  5,  264;  1904. 
Athanasiadis,  Lond.  Elec.,  61,  873;  1906. 

5  Phil.  Mag.,  16,  478;  1840. 


70  THE  ELECTRIC  ARC 

there  is  an  excess  of  current  flowing  from  the  carbon.  This 
called  attention  again  to  the  phenomenon  which  had  been 
noticed  by  Grove  and  further  experiments  have  shown  that 
in  general  when  the  electrodes  are  of  different  substances, 
the  current  flows  more  easily  in  one  direction  than  in  the 
other.1  For  example,  it  flows  more  easily  from  any  metal 
to  carbon  than  in  the  reverse  direction;  more  easily  from 
cored  carbon  to  solid  than  from  solid  to  cored;  and  more 
easily  from  a  carbon  that  is  easily  kept  hot  to  one  that 
is  not,  as  a  rotating  carbon  disk,  than  in  the  opposite 
direction. 

The  explanation  of  this  is  as  follows:  The  conductivity 
of  the  arc  depends  on  the  kind  of  vapor  in  the  arc  and 
also  upon  the  ease  with  which  the  cathode  can  be  kept  at 
a  high  temperature,  but  does  not  depend  to  any  large  ex- 
tent on  the  temperature  of  the  anode.  If  the  anode  gives 
off  a  conducting  vapor  when  heated,  this  vapor  will  affect 
the  conductivity,  but  the  anode  does  not  directly  affect  the 
conductivity  to  more  than  a  very  small  extent.  These 
facts  will  be  discussed  more  fully  at  a  later  point,  but  may 
be  accepted  for  the  present  in  explaining  the  phenomena 
under  discussion. 

If  we  apply  these  facts  to  the  arc  between  iron  and  car- 
bon, for  example,  we  find  that  the  current  flows  more 
easily  from  iron  to  carbon;  first,  because  the  conduc- 
tivity of  the  iron  vapor  is  greater  than  that  of  the  carbon 
vapor,  and  there  is  more  of  this  vapor  sent  into  the  arc 

1  See  also  the  following : 

Gold,  Wien.  Sitzungsber.,  104,  2A,  814;   1895. 
Petlinelli,  Rend.  Ace.  Lind.,  (5),  5,  118  and  136;    1896. 
Von  Lang,  Wied.  Ann.,  63,  191;    1897. 
Cassuto,  Phys.  ZS.,  5,  263;   1904. 


ARC  IN  AIR  BETWEEN  OTHER   SUBSTANCES  71 

when  the  anode  is  iron,  since  there  is  more  heat  developed 
near  the  anode  with  arcs  in  air  than  near  the  cathode. 
That  the  conductivity  of  iron  vapor  is  greater  than  that 
of  carbon  is  shown  by  the  fact  that  the  drop  in  potential 
across  an  arc  having  both  terminals  iron  is  much  less  than 
that  about  an  arc  having  both  terminals  carbon. 

This  part  of  the  explanation  of  the  greater  current  from 
iron  to  carbon  was  given  by  Arons,1  but  the  difficulty  of 
keeping  the  iron  hot  enough  to  be  the  cathode  must  also 
be  considered.  As  will  be  shown  in  following  paragraphs, 
it  is  always  necessary  to  have  a  point  on  the  cathode  at 
a  very  high  temperature.  Manifestly,  it  is  harder  to  keep 
a  spot  on  iron  very  hot  than  one  on  carbon,  first  be- 
cause iron  conducts  heat  more  rapidly  than  carbon,  and 
secondly  because  iron  melts  and  vaporizes  more  readily 
than  carbon,  and  heat  is  lost  in  producing  these  changes. 
In  order  to  furnish  this  heat  the  cathode  drop  must  be 
large. 

The  need  of  this  last  consideration  will  perhaps  be  more 
apparent  in  the  case  of  discharge  between  a  stationary 
carbon  rod  and  a  carbon  disk  kept  at  a  lower  temperature 
by  rotating  it.  Here  the  current  is  the  greater  when  the 
moving  carbon  is  the  anode.  Arons'  explanation  is  not  in 
this  case  sufficient,  since  the  vapor  in  the  arc  will  be  carbon 
vapor,  whichever  way  the  current  flows.  On  the  other 
hand,  the  second  consideration  applies,  for  it  will  clearly  be 
easier  to  keep  the  stationary  carbon  hot  than  the  moving 
one,  so  that  the  current  will  be  larger  when  the  stationary 
carbon  is  cathode. 

A  few  observations  made  by  myself  on  the  cathode  and 
anode  drops  in  a  carbon-iron  arc  are  quite  in  harmony  with 
1  Wied.  Ann.,  57,  195;  1896. 


THE   ELECTRIC   ARC 


this  view.  The  introduction  of  a  carbon  pencil  into  such 
an  arc  makes  it  very  unsteady  and  changes  the  vapor  in 
the  arc  to  some  extent,  so  that  the  values  given  below  can 
not  be  considered  accurate.  They  are,  however,  of  some 
value.  These  observations  were  made  with  a  constant 
length  and  constant  current. 


Anode. 

Cathode. 

Anode 
drop. 

Cathode 
drop. 

Carbon 

Carbon 

38 

13 

Iron 

Carbon 

14 

17 

Carbon 

Iron 

12 

21 

In  the  first  case  both  electrodes  are  carbon.  In  the 
second  the  anode  is  iron  and  the  vapor  from  this  is  highly 
conducting  and  causes  a  large  decrease  in  the  drop  in 
potential  near  the  anode.  The  cathode  drop  is  slightly 
greater  than  when  both  electrodes  are  carbon,  the  reason, 
no  doubt,  being  that  the  iron  anode  is  cooler  than  the 
carbon  anode,  and  allows  the  cathode  to  cool  off  more 
rapidly,  requiring  a  large  cathode  drop  to  maintain  the 
temperature  of  the  cathode. 

In  the  third  case  there  is  still  enough  iron  vapor  in  the 
arc  to  cause  a  small  anode  drop,  but  the  heat  is  conducted 
away  from  the  iron  cathode  so  rapidly  that  it  requires  a 
still  higher  cathode  drop  to  maintain  the  temperature  of 
the  iron  at  the  required  point. 


CHAPTER    IV. 


THE  ARC  IN  AIR  WITH  PRESSURES   GREATER  OR  LESS 
THAN  ONE  ATMOSPHERE. 

Pressures   Greater  than  One  Atmosphere.  —  But  few 

experiments  have  been  performed  with  the  arc  in  a  gas 
under  pressure.  Wilson  and  Fitzgerald1  found  that  with 
pressures  greater  than  one  atmosphere  fumes  of  N02  were 
formed  and  that  these  became  very  plentiful  when  the 


2  4  6  8  10  12 

ATMOSPHERES 

FIG.    18. 

pressure  was  as  great  as  100  pounds  per  square  inch. 
Duncan,  Rowland  and  Todd2  found  that  the  apparent  re- 
sistance of  the  arc  increased  as  the  pressure  was  increased, 
as  is  shown  in  Fig.  18.  The  curves  in  this  give  the  voltage 

1  Proc.  Roy.  Soc.,  60,  377;  1896. 

2  Elektrot.  ZS.,  14,  603;  1893. 

73 


74  THE  ELECTRIC  ARC 

between  the  terminals  of  the  arc  with  different  pressures 
of  the  gas,  the  current  being  maintained  at  6  amperes. 

Pressures  Less  than  One  Atmosphere.  —  While  the  arc 
in  a  vacuum  has  no  great  commercial  value,  it  gives  us 
much  information  which  is  useful  in  forming  a  theory  of 
the  arc,  for  with  very  low  pressures  there  are  no  com- 
plications due  to  chemical  actions,  the  temperature  is 
sufficiently  low  so  that  small  exploring  wires  may  be  used 
without  appreciably  distorting  the  field,  and  the  existence 
of  striations  and  cathode  rays  shows  the  similarity  between 
this  form  of  discharge  and  those  having  much  smaller 
currents. 

The  earliest  experiments  on  an  arc  in  a  vacuum  were  per- 
formed before  the  distinction  between  arc  and  spark  was 
made  and  with  many  of  these  experiments  it  is  impossible 
to  determine  which  form  of  discharge  was  really  used. 

Thus,  an  experiment  was  performed  by  Davy  in  iSog1 
to  ascertain  whether  any  heat  sensible  to  a  thermometer 
is  produced  by  the  electric  flame  in  a  vacuum,  but  it  can 
not  be  definitely  stated  whether  this  was  an  arc  or  a  glow 
discharge.  The  same  statement  must  be  made  of  the  work 
by  Van  Breda.2 

1  Mrs.  Ayrton's  "  Electric  Arc,"  p.  25. 

2  C.  R.,  23,462;  1846. 

Note.  — The  work  of  De  la  Rive  (Phil.  Trans.,  1847,  part  i)  appears  to 
have  been  with  an  arc,  while  that  of  De  la  Rue  and  Miiller  (Phil.  Trans., 
171,  A,  65;  1880;  Proc.  Roy.  Soc.,  29,  286;  1879)  was  apparently  on  a 
continuous  glow  discharge,  since  the  current  which  they  used  was  very 
small  and  the  voltage  several  thousand  volts.  Stenger,  in  1885  (Wied. 
Ann.,  25,  31;  1885),  gives  four  differences  between  the  arc  and  the  glow 
discharge  in  a  vacuum,  but  only  one  of  these,  namely,  that  the  gaseous 
portion  has  less  resistance  in  the  arc  than  in  the  glow  discharge,  can  be 
said  to  be  correct,  while  some  of  the  more  important  differences  were  not 
noted. 


PRESSURES  GREATER  OR  LESS  THAN  ONE  ATMOSPHERE    75 

Carbon  Arc  in  a  Vacuum.  —  In  more  recent  work  we 
find  more  definite  statements  about  the  conditions  and 
we  can  be  sure  of  the  form  of  discharge  being  used.  The 
greater  part  of  this  work  has  been  with  carbon  elec- 
trodes. When  the  pressure  about  such  an  arc  is  dimin- 


FIG.  19. 

ished,  the  anode  becomes  slightly  less  luminous  and  the 
cross  section  of  the  luminous  gas  becomes  somewhat 
greater,  but  the  appearance  is  not  greatly  changed  until  a 
pressure  of  only  a  few  millimeters  is  reached.  At  that 
point  a  very  decided  change  occurs.  Under  certain  con- 
ditions striations  appear,  as  shown  in  Fig.  19.  As  the 


76 


THE  ELECTRIC   ARC 


pressure  is  diminished  the  number  of  striations  becomes 
less,  as  is  shown  in  Fig.  20.  With  still  lower  pressures  the 
striations  disappear  and  the  glow  at  the  anode  moves 
about  in  a  very  erratic  way.  At  times  it  appears  as  a 
ring  about  the  anode  a  few  centimeters  above  the  end,  as 


FIG.  20. 


in  Fig.  21.     Occasionally  two  rings  of  this  kind  have  been 
noticed. 

With  pressures  less  than  5  mm.  this  ring  also  disappears 
and  the  arc  consists  of  a  bright  spot  on  the  cathode  from 
which  cathode  rays  appear  to  come  and  a  faint  lumi- 
nosity in  the  space  through  which  these  rays  happen  to 


PRESSURES  GREATER  OR  LESS  THAN  ONE  ATMOSPHERE    77 

stream.  When  this  state  is  reached  the  arc  is  not 
appreciably  affected  by  varying  the  distance  between 
the  electrodes. 

The  voltage  required  to  maintain  an  arc  in  a  vacuum  is 
much  less  than  that  required  to  maintain  one  in  air.     The 


FIG.  21. 


1    Curve  i  represents  the  anode  drop  at  different 
curve  2  the  cathode  drop,  curve  3  the  electric 


results  of  some  observations  taken  by  myself  are  given  in 
Fig.  22. 
pressures 

force  per  centimeter  and  curve  4  the  total  potential  dif- 
ference between  the  terminals.      The  observations  were 

1  Phys.  Rev.,  19,  120;  1904,  and  20,  368;  1905. 


THE  ELECTRIC  ARC 


100 


200  300  400  500 

PRESSURE  IN  MM. 

FlG.  22. 


600 


700 


50  100  150  200  250  300  350  400  450  500  550  600  650  700  750 

PRESSURE  IN  MM. 
FIG.  23. 


PRESSURES  GREATER  OR  LESS  THAN  ONE  ATMOSPHERE    79 

taken  with  a  current  of   10  amperes  and  a  distance  of 
2  mm.  between  solid  carbons.1 


10 


3  4 

LENGTH  IN  M,M. 
FIG.  24. 

A  more  extended  examination  of  the  arc  in  a  vacuum 
has  been  made  by  Hoerburger.2  His  results  are  shown  in 
Figs.  23  and  24.  The  first  gives  the  relation  between  volt- 
age and  pressure  of  the  gas  for  different  lengths  of  the  arc, 
the  current  being  6  amperes.  Fig.  24  shows  the  relation 

1  As  has  been  shown  in  Fig.  18,  Duncan,  Rowland  and  Todd  found 
with  longer  arcs  an  increase  in  voltage  when  the  pressure  was  reduced 
below  one  atmosphere.     This,  however,  is  contrary  to  the  observations  of 
all  other  experimenters. 

2  Dissertation  Griesswald.     Beib.,  29,  883;  1905. 


8o 


THE  ELECTRIC  ARC 


between  voltage  and  length  of  the  arc  for  different  pres- 
sures. The  voltage  is  here  shown  to  be  a  linear  function 
of  the  length  of  the  arc  for  all  pressures.  This  is  expressed 
by  the  formula  E  =  a  +  blt  where  a  and  b  are  quantities 
depending  on  the  pressure  of  the  gas.  a  would  be  approx- 


55 

^ 

>-  — 

-«_ 

—  0 

40 
35 

r; 

^__^, 

^—-  - 

>-  — 

-i 

6 

^ 

30 
25 

7 

3. 

/ 

20 

15 

I 

^. 
1 

0. 

1  0 

5 

,5^ 

s 


50  100  150  200  250  300  350  400  450  500  550600  650  700750 

PRESSURE  IN  MM. 
FIG.  25. 

imately  the  same  as  the  sum  of  the  anode  and  cathode 
drops,  and  b  the  same  as  the  electric  force  through  the  arc. 
Their  values  for  different  pressure  are  plotted  in  Fig.  25. 
The  values  for  a  vary  in  the  same  way  as  those  for  the 
cathode  and  anode  drop,  as  shown  in  Fig.  22,  and  the 
values  for  b  in  the  same  way  as  the  values  for  the  electric 
force  as  found  by  myself.1 


1  Phys.  Rev.,  19,  122;  1904. 


PRESSURES  GREATER  OR  LESS  THAN  ONE  ATMOSPHERE    8^ 

The  arc  in  a  vacuum  has  a  lower  temperature  than  that 
in  air.1  This  has  been  shown  by  placing  a  platinum  wire 
0.3  mm.  in  diameter  in  the  arc.  At  atmospheric  pressures 
this  would  be  melted  in  a  fraction  of  a  second.  When 
the  pressure  of  the  surrounding  gas  is  4  mm.,  the  wire 
is  not  melted.  With  still  lower  pressures  it  gathers  a 
deposit  of  carbon.2 

Metal  Arc  in  a  Vacuum.  —  The  arc  between  metals  in  a 
vacuum  has  much  the  same  appearance  as  that  between 
carbons  in  a  vacuum,  except  that  with  the  former  the 
striations  appear  to  be  even  more  peculiar  than  with  the 
latter.3  The  character  of  such  an  arc  does  not  depend  to 
any  great  extent  on  the  kind  of  metal  used  for  the  anode. 
In  fact,  if  the  anode  does  not  become  so  hot  as  to  send 
vapor  into  the  tube,  it  appears  to  have  no  effect  on  the 
discharge,  so  that  any  metal  may  be  satisfactorily  used 
for  this  electrode.  Quite  the  opposite  of  this  is  true  con- 
cerning the  cathode.  If  the  cathode  is  a  metal  which 
melts  easily,  there  is  no  difficulty  in  maintaining  the  arc 
with  very  low  pressures  of  the  gas,4  but  metals  with  high 
melting  points  can  not  be  used  for  the  cathode.5  It  is, 
for  example,  impossible  to  maintain  an  arc  with  platinum, 
iron,  nickel,  copper  or  silver  for  the  cathode  when  the  pres- 
sure of  the  gas  is  less  than  i  mm.  and  the  impressed  E.M.F. 
is  no  more  than  100  volts.  Apparently  the  higher  the 
melting  point  of  the  metal  used,  the  more  difficult  it  is  to 


1  Grove,  Phil.  Mag.,  16,  479;   1840. 

2  Phys.  Rev.,  19,  123;    1904. 

3  Herwig,  Pogg.  Ann.,  149,  523;   1873. 
Arons,  Ann.  d.  Phys.,  i,  711;   1900. 

4  Stark  and  Kuch,  Phys.  ZS.,  6,  438;   1905. 
6  Phys.  Rev.,  20,  369;    1905. 


82 


THE  ELECTRIC  ARC 


maintain  the  arc.    The  following  is  a  table  of  cathode  drop 
with  the  metals  which  could  be  used  in  a  vacuum. 


Metal. 

Cathode  drop. 

Aluminum 

19 

Antimony 

8 

Zinc 

9 

Lead 

8 

Cadmium 

7 

Bismuth 

6 

Tin 

8 

This  difficulty  does  not  exist  with  oxides  of  metals.  An 
arc  can  easily  be  maintained  in  a  vacuum  with  oxides  for 
the  cathode.  This  is  especially  true  of  calcium  oxide. 
On  the  other  hand  calcium  sulphide  seems  to  have  no 
effect,  nor  the  super-oxides  of  lead,  manganese  or  zinc.1 

An  attempt  was  made  by  Arons  to  form  an  arc  between 
terminals  of  Wood's  metal  kept  liquid  by  being  placed  in 
a  water  bath  near  the  boiling  point,  but  in  every  case  the 
tube  broke  almost  as  soon  as  the  lamp  was  started.  In 
only  one  case  was  it  possible  to  take  a  reading  of  the  current 
and  potential  difference.  At  that  time  the  potential  dif- 
ference was  between  55  and  65  volts  and  the  current  about 
2  amperes. 

The  results  with  an  alloy  of  sodium  and  potassium  were 
somewhat  better.  Some  of  the  lamps  which  contained 
this  also  broke  on  first  starting  them;  others  lasted  suffi- 
ciently long  to  make  observations.  He  found  it  possible 
to  have  currents  from  2  to  1 5  amperes  with  a  potential  dif- 
ference between  7  and  8  volts.  Similar  lamps  which  lasted 
several  hours  were  made  by  Weintraub.2 

1  Stark,  Phys.  ZS.,  5,  81;   1904. 

2  Phil.  Mag.,  (6),  7,  114;   1904- 


PRESSURES  GREATER  OR  LESS  THAN  ONE  ATMOSPHERE    83 

Arc  in  Other  Gases  than  Air.  —  There  have  been 
a  number  of  experiments  performed  on  the  arc  in  other 
gases  than  air  with  no  great  agreement  as  to  results. 
About  the  only  point  on  which  there  is  agreement  is  that 
it  is  more  difficult  to  maintain  an  arc  in  hydrogen  than 
in  air.1 

In  regard  to  the  amount  of  potential  difference  needed 
with  the  arc  in  hydrogen  the  following  data  have  been 
given.  Arons  could  not  maintain  such  an  arc  on  a  circuit 
of  105  volts,  unless  the  pressure  of  the  gas  was  less  than 
one  atmosphere.  In  some  work  by  myself2  it  was  found 
that  the  voltage  at  the  terminals  of  the  arc  was  100  volts 
with  the  arc  in  hydrogen  at  a  pressure  of  70  cm.  With 
graphite  terminals  under  the  same  conditions  the  voltage 
was  130  volts.  Stark,  Retschinsky  and  Schaposchnikoff 
give  similar  data  for  the  carbon  arc  in  hydrogen  and  some- 
what larger  values  with  the  copper  arc  in  hydrogen.3 
Malcolm  and  Simon  using  small  currents  and  a  distance 
between  the  electrodes  of  4  mm.  give  the  equation  E  = 
60  +  1 8o/7. 

With  metals  in  hydrogen  they  found  it  impossible  to 

1  Grove,  Phil.  Mag.,  16,  480;   1840. 
Matteucci,  C.  R.,  30,  201;   1850. 
Herwig,  Pogg.  Ann.,  149,  523;   1873. 

Wilson  and  Gray,  Proc.  Roy.  Soc.,  60,  377;   1897. 

Arons,  Ann.  d.  Phys.,  I,  700;  1900. 

Upson,  Lond.  Elec.,  60,  58;  1908.  Phil.  Mag.,  (6),  14,  126;  1908. 
S.  P.  Thomson  states  that  the  voltage  of  the  arc  in  oxygen,  nitrogen, 
hydrogen  and  other  gases  was  the  same  to  within  one  volt,  the  current  in  each 
case  being  10  amperes.  (Lond.  Elec.,  29,  460;  1892.)  This  result  is  so 
different  from  that  of  all  other  experimenters  that  we  must  consider  it 
incorrect. 

2  Phys.  Rev.,  20,  374;    1905. 

3  Ann.  d.  Phys.,  18,  223;    1906. 


84 


THE   ELECTRIC  ARC 


measure  the  potential  difference,  unless  the  metals  were 
kept  cool,  because  they  melted  away  so  rapidly.  They 
avoided  this  difficulty  by  running  a  current  of  water 
through  the  inside  of  the  electrode.  With  nickel  it  re- 
quired from  500  to  600  volts  in  hydrogen  while  the  corre- 
sponding values  in  air  were  less  than  100  volts. 

The  only  other  gas  with  which  experiments  have  been 
made  to  any  extent  is  nitrogen.  The  voltages  required 
with  this  do  not  greatly  differ  from  those  required  with 
the  arc  in  air.  The  first  data  with  the  arc  in  nitrogen  were 
given  by  Arons.  The  comparison  of  his  results  with  those 
which  had  been  found  by  von  Lang  for  the  arc  between 
metal  in  air  is  given  in  the  following  table.  The  data  are 
given  for  a  distance  between  the  electrodes  of  1.4  mm.  and 
a  current  of  4  amperes. 


Metal. 

Potential  difference  in  volts. 

Remarks. 

In  air  (v.  Lang)  . 

In  N.  (Arons)  . 

Ag.  . 

21 
23 
25 
25 
29 
36 
39 

? 

21-22 
21-22 
29-32 
19-22 
29-31 
26-29 
18 
21-25 

With  small  currents. 

With  large  currents. 
With  small  currents. 

Zn  

Cd  

Cu  
Fe  

Pt 

Al  
Pb 

Mg  

Arons  found  it  impossible  to  maintain  an  arc  in  nitrogen 
between  silver  terminals  on  a  ic>5-volt  circuit  with  6  ohms 
in  the  circuit.  On  the  other  hand  Malcolm  and  Simon 
found  the  voltage  with  silver  terminals  only  about  20  volts 
higher  in  nitrogen  than  in  air. 


PRESSURES  GREATER  OR  LESS  THAN  ONE  ATMOSPHERE    85 

The  same  experimenters  give  the  following  equations 
when  using  carbon  electrodes  4  mm.  apart: 

In  air  E  =  49.5  +  31.5/7;     in  nitrogen  E  =  62  +  30/7. 

Grau  and  Russ1  examined  the  arc  in  different  gases  for 
small  currents  and  with  the  distance  of  5  cm.  between 
electrodes.  The  order  of  the  gases  when  arranged  with 
respect  to  increasing  potential  differences  was  N2,  air,  CO, 
S02,  O2,  CO2  and  H2.  The  values  for  nitrogen  varied  from 
3450  volts  when  the  current  was  0.05  ampere  to  2075  volts 
when  it  was  0.112  ampere.  For  hydrogen  the  value  of  the 
potential  difference  varied  from  6600  volts  with  a  current 
of  0.05  ampere  to  5250  volts  with  a  current  of  0.121  ampere. 
This  was  called  by  them  an  arc,  but  the  values  of  both 
the  current  and  the  potential  difference  are  so  different 
from  those  of  the  ordinary  arc  that  one  would  need  to  know 
the  magnitude  of  the  cathode  drop  in  order  to  decide 
whether  this  should  be  called  an  arc  or  a  spark. 

Experiments  were  performed  by  Weedon2  on  the  arc 
between  water-cooled  copper  electrodes  for  the  purpose  of 
determining  whether  there  is  any  law  regarding  the  elec- 
trodes of  the  arc  similar  to  Faraday's  laws  of  electrolysis. 
With  such  electrodes  in  air  using  a  current  of  2  amperes 
for  ij  hr.  with  a  potential  difference  of  50  volts  there  was 
a  gain  of  weight  of  the  anode  of  0.023  £•>  and  of  the  cathode 
of  0.004  g.  This  is  not  more  than  ^-Q  of  the  amount 
which  would  have  been  transferred  in  electrolysis  and  this 
is  probably  due  to  oxidation  at  high  temperatures  rather 
than  to  any  chemical  action. 

1  ZS.  f.  Elektrochemie,  13,  345;    1907. 

2  Paper    presented    at    the    Electrochem.    Soc.,    Washington,    D.  C., 
April,  1904. 


86  THE  ELECTRIC  ARC 

With  the  same  electrodes  in  hydrogen  and  with  a  form 
of  discharge  which  required  only  0.35  ampere  and  a  poten- 
tial difference  of  about  300  volts  he  found  that  the  cathode 
lost  0.004  g-  in  Jl  hr.  and  the  anode'gained  an  equal  amount, 
but  it  is  a  question  whether  this  was  really  an  arc  or  not, 
so  that  no  definite  conclusion  can  be  drawn.  But  the  two 
experiments  would  at  least  show  that  nothing  as  simple 
as  Faraday's  laws  will  apply  to  the  loss  of  material  of  the 
electrodes  of  the  arc. 

The  only  measurements  which  have  been  published  con- 
cerning the  potential  in  different  parts  of  the  arc  in  other 
gases  than  air  were  made  by  myself  when  working  with 
the  arc  in  hydrogen.  It  was  found  that  with  graphite 
terminals  the  larger  drop  was  at  the  cathode.  When  the 
pressure  of  the  gas  was  700  mm.,  the  anode  drop  was 
57  volts  and  the  cathode  drop  65  volts.  On  the  other  hand 
with  the  carbon  arc  in  hydrogen  by  far  the  greater  drop 
was  at  the  anode.  With  700  mm.  of  pressure  the  anode 
drop  was  85  volts  and  the  cathode  drop  15  volts. 

With  lower  pressures  the  behavior  of  the  arc  is  much  the 
same  as  it  is  with  low  pressures  of  air.  The  principal  differ- 
ences are  found  when  using  low  pressures  of  hydrogen. 
Stria tions  are  much  more  prominent  than  they  are  when 
the  residual  gas  is  air  and  these  appear  at  much  higher 
pressures.  With  pressures  of  approximately  20  mm.  I 
found  four  distinct  forms  of  the  arc,  three  of  these  showing 
stria  tions. 


CHAPTER  V. 

THE  MERCURY  ARC. 

THE  mercury  arc  is  an  arc  in  a  vacuum  having  mercury 
for  the  cathode  and  either  mercury  or  any  other  substance 
which  does  not  form  an  amalgam  with  it  for  the  anode. 
Tubes  containing  such  arcs  are  usually  called  mercury 
vapor  lamps.  This  lamp  was  first  studied  by  Arons  in 
1892 x  and  was  developed  by  Cooper  Hewitt  into  a  valu- 
able commercial  form  in  1902?  The  commercial  use  has 
added  much  interest  to  the  study  of  this  arc  and  it  is 
also  by  far  the  best  form  for  scientific  purposes.  One  can 
not,  for  example,  begin  to  explain  any  of  the  phenomena 
of  the  arc  without  having  some  idea  of  the  cause  of  its 
electrical  conductivity.  This  requires  some  knowledge  of 
the  temperature  of  the  vapor  and  of  the  electric  force 
through  this  vapor,  and  the  mercury  arc  offers  the  best 
chance  for  accurate  measurements  of  such  quantities. 
With  this  there  are  no  complications  due  to  chemical 
action  and  the  temperature  is  such  that  detailed  measure- 
ments can  here  be  made  with  fine  wires  which  do  not 
seriously  change  the  character  of  the  discharge.  For  this 
reason  this  arc  is  described  more  fully  than  any  other  in  the 
following  pages. 

For  commercial  use  the  mercury  arc  has  several  impor- 
tant advantages.  The  first  of  these  is  that  the  light  is  not 

1  Wied.  Ann.,  47,  767;   1892. 

2  Trans.  Amer.  Elec.  Inst.,  19,  59,  and  20,  929;   1902. 

87 


88  THE   ELECTRIC  ARC 

so  concentrated  as  in  other  forms.  Practically  all  of  the 
light  comes  from  the  vapor,  and  this  is  usually  several 
inches  in  length  and  about  one  inch  in  diameter.  Again 
it  has  a  high  efficiency  and  does  not  require  any  attention. 
There  is  no  occasion  to  renew  electrodes  nor  to  remove 
products  of  combustion.  As  long  as  the  tube  keeps  out 
the  air  it  is  in  working  order  and  manufacturers  claim  a  life 
of  5000  hours  for  the  lamp  under  favorable  conditions. 
Lastly  it  does  not  require  any  elaborated  feeding  mechanism. 
Nothing  could  be  simpler  than  the  Cooper  Hewitt  form  of 
this  lamp. 

On  the  other  hand  it  has  the  disadvantage  of  giving  an 
unpleasant  light.  It  is  not  so  much  that  the  light  appears 
to  one  looking  at  it  to  be  different  from  white  light,  as  that 
it  gives  the  wrong  color  to  objects  which  it  illuminates. 
This  is  due  to  the  absence  from  its  spectrum  of  some  im- 
portant colors.  Its  spectrum  is  a  line  spectrum  in  which 
only  a  few  lines  are  prominent.  It  is  lacking  in  red,  while 
the  green  is  very  prominent.  As  a  result  it  gives  to  the 
human  face,  for  example,  a  disagreeable  and  lifeless  appear- 
ance. The  lamp  is,  however,  of  much  value  in  certain 
special  uses,  as  in  a  drafting  room,  where  only  the  distinc- 
tion between  black  and  white  is  desired,  or  in  photographic 
work,  where  the  strong  violet  rays  are  of  use. 

The  first  arc  between  mercury  terminals  of  which  we 
have  any  record  was  one  described  by  Wey.1  This,  how- 
ever, was  an  arc  in  the  air  and  showed  nothing  of  especial 
interest. 

The  first  mercury  arc  in  a  vacuum  was  described  by 
Arons  in  1892. 2  The  arc  was  in  an  inverted  U-shaped  glass 

1  Dingler's  Polytechnic.  Journ.,  157,  399;   1860,  and  159,  46;   1861. 

2  Wied.  Ann.,  47,  767,  1892. 


THE  MERCURY  ARC 


89 


tube  2  cm.  in  diameter  and  12  cm.  long.  Platinum  ter- 
minals were  sealed  into  the  two  legs  and  these  were  nearly 
filled  with  mercury.  The  arc  was  started  by  tipping  the 
tube  until  the  mercury  in  the  two  legs  flowed  together  and. 
then  tipping  it  back  to  its  original  position.  The  following 
table  gives  the  relation  between  current  and  potential 
difference  which  he  found  when  the  pressure  of  the  residual 
gas  was  only  a  fraction  of  a  millimeter. 


Current  in  amperes 

ii 

9 

7 

5  5 

3 

2 

I  4 

o  8 

o  5 

Potential  dif  .  ,  in  volts  

17-5 

17 

16.5 

16 

15-3 

14 

20 

28 

40 

With  currents  greater  than  1.4  amperes  the  tube  was 
filled  with  light.  At  the  cathode  there  was  a  spot  of  in- 
tense light  which  was  in  constant  motion.  With  small 
currents  stratifications  occasionally  appeared. 

The  presence  of  small  amounts  of  air  or  hydrogen  did 
not  greatly  affect  the- relation  between  the  current  and  the 
potential  difference.  For  example,  when  the  pressure  of 
the  remaining  gas  was  5  mm.,  there  was  a  current  of 
8.5  amperes  with  a  potential  difference  of  18  volts,  which 
is  but  little  different  from  that  given  above  for  the  same 
current.  In  that  case,  however,  the  light  did  not  fill  all 
of  the  tube,  but  appeared  as  a  band  in  the  central  part, 
and  the  glass  became  heated  very  quickly. 

A  few  years  later  Arons  found  that  the  mercury  vapor 
loses  its  conductivity  very  quickly  after  the  arc  has  been 
extinguished  and  that  it  is  not  possible  to  have  an  alter- 
nating-current arc  with  such  a  lamp.1 

The  commercial  form  of  this  arc  as  developed  by  Cooper 
Hewitt  is  shown  in  Fig.  26.  In  this  lamp  both  terminals 
are  mercury.  It  is  started  by  tipping  the  tube  so  that  the 

1  Wied.  Ann.,  57,  192;  1896,  and  58,  73;  1896. 


9o 


THE   ELECTRIC   ARC 


mercury  in  the  lower  bulb  flows  along  and  makes  contact 
with  that  in  the  upper  one.  The  tube  is  then  tipped  back 
into  the  position  shown  in  the  figure,  which  breaks  the 
contact  and  starts  the  arc. 


FIG.  26. 

The  mercury  lamp  made  by  the  General  Electric  Com- 
pany is  shown  in  Fig.  27.  Here  the  anode  is  a  cylinder  of 
carbon  and  the  arc  is  started  by  a  fine  carbon  filament 
running  through  the  lamp  and  dipping  into  an  iron  cup 
which  floats  on  the  mercury  at  the  bottom  of  the  tube.  As 
soon  as  the  current  is  started  this  cup  is  drawn  down  by 
a  solenoid  about  the  outside  of  the  tube,  through  which 
the  current  flows.  As  it  is  drawn  down,  an  arc  is  started 


THE  MERCURY  ARC 


91 


at  the  bottom  of  the  filament,  which  quickly  extends  the 
whole  length  of  the  tube,  since  the  resistance  of  the  carbon 
filament  is  much  greater  than  that  of  the  mercury  vapor 
after  the  arc  is  started. 


FIG.  27. 

Temperature  of  the  Mercury  Arc.  —  As  has  been  stated 
the  mercury  arc  affords  better  opportunities  than  other 
arcs  for  the  accurate  measurements  of  those  quantities 
which  are  important  in  forming  a  theory  of  the  discharge. 
While  this  is  true,  there  are  still  several  of  these  about  which 
we  are  more  or  less  ignorant.  Either  the  different  ob- 
servers have  recorded  different  results,  or  else  some  valid 
criticism  may  be  made  on  the  methods  used. 


92  THE  ELECTRIC  ARC 

One  of  these  quantities  is  the  temperature  of  the  mercury 
arc.  Nothing  would  seem  simpler  than  to  insert  a  ther- 
mometer or  thermojunction  in  the  mercury  vapor  and 
observe  its  temperature.  There  are,  indeed,  several  who 
have  made  such  measurements.  Thus  Arons  measured  this 
temperature  by  means  of  a  mercury  thermometer  and 
found  that  it  varied  from  285°  C.  to  515°  C.  Wills1  meas- 
ured it  with  a  thermojunction  and  found  values  varying 
from  83°  C.  to  297°  C.,  depending  on  the  length  of  time 
that  the  arc  had  been  running  and  on  the  density  of  the 
mercury  vapor.  Knipp  also  measured  this  temperature 
with  a  thermojunction  and  showed  that  the  temperature 
increases  rapidly  as  the  pressure  of  the  vapor  increases.2 
However,  both  the  thermometer  and  the  thermojunction 
give  temperatures  which  are  too  low.  Both  radiate  some 
heat  and  conduct  some  away  and  must  be  cooler  than  the 
vapor  in  order  to  receive  heat  from  it.  Arons,  therefore, 
made  a  further  test  by  placing  a  fine  platinum  wire  in  the 
vapor  of  the  arc.  He  found  that  this  was  quickly  melted. 
There  is,  however,  the  possibility  that  the  platinum  wire 
first  formed  an  amalgam  with  the  mercury  and  that  this 
caused  the  wire  to  melt  at  a  comparatively  low  temperature. 
I  have,  therefore,  repeated  the  experiment  using  a  glass 
fiber  and  find  that  this  also  can  be  melted  in  the  mercury 
arc,  but  even  here  we  are  not  on  sure  ground,  for  the  glass 
may  receive  its  heat  from  the  moving  electrons  and  not 
from  the  molecules  of  the  vapor. 

Arons  endeavored  to  compute  the  temperature  of  the 
mercury  vapor.  We  know  approximately  the  amount 
of  gas  in  the  tube,  its  specific  heat  and  the  rate  at  which 

1  Phys.  Rev.,  19,  65;    1904. 

2  Phys.  Rev.,  24,  446;   1907,  and  31,  97;   1910. 


THE  MERCURY  ARC  ^3 

energy  is  given  to  it.  If  we  had  any  definite  knowledge 
concerning  the  relation  between  the  temperature  of  a 
luminous  vapor  and  the  rate  at  which  it  radiates  heat, 
it  would  be  a  simple  matter  to  make  this  computation,  but 
while  we  know  something  about  the  rate  at  which  a  non- 
luminous  vapor  radiates  heat,  there  is  a  small  portion  of 
the  gas  which  is  luminous  and  this  radiates  energy  at  a 
very  much  greater  rate.  Arons  did  indeed  make  some 
assumption  concerning  this  and  arrived  at  the  conclusion 
that  the  temperature  of  the  vapor  must  be  4000°  C.  or 
5000°  C.  This  certainly  is  much  too  high,  so  that  it  would 
appear  that  theoretical  considerations  help  us  but  little 
with  this  problem. 

For  the  same  reason  we  can  not  accept  the  measurements 
of  this  temperature  made  by  Fery,1  who  compared  the 
intensity  of  the  light  in  different  parts  of  the  spectrum  of 
this  arc  with  corresponding  parts  of  the  spectrum  of  the 
carbon  arc  and  concluded  that  the  temperature  of  the 
mercury  vapor  was  3500°  C.  This  temperature  may 
possibly  be  the  correct  temperature  for  the  luminous  part 
of  the  vapor,  but  can  hardly  be  correct  for  the  non-luminous 
part. 

It  indeed  seems  more  probable  that  the  measurements 
made  with  a  thermojunction  are  not  far  from  the  correct 
value,  at  least  for  pressures  of  several  millimeters.  How- 
ever, as  the  density  of  the  vapor  becomes  less  the  error  will 
become  greater  and  there  is  no  means  known  for  deter- 
mining the  exact  amount  of  the  error. 

Characteristic  Curves  for  the  Mercury  Arc.  —  A  knowl- 
edge of  the  relation  between  the  current  and  the  voltage  is 
also  important  in  forming  a  theory  of  the  arc,  and  it  is  also 

1  Soc.  Franc.  Phys.  Bull.,  No.  3,  305;   1907. 


94  THE  ELECTRIC  ARC 

difficult  to  determine  this  relation.  It  is  not  possible  to 
change  the  current  with  the  arc  in  a  tube  without  changing 
the  pressure  of  the  vapor  through  which  the  current  is 
passing,  and  a  change  in  the  pressure  of  the  vapor  will  in 
itself  cause  a  change  in  the  voltage  required  irrespective 
of  any  effect  which  the  current  may  have. 

Moreover,  the  amount  of  change  in  the  vapor  pressure 
depends  on  several  factors.  If,  for  example,  the  tube 
containing  the  arc  is  connected  to  a  pump  the  vapor  pro- 
duced by  the  arc  passes  into  other  parts  of  the  apparatus 
where  it  is  rapidly  condensed  and  the  pressure  in  the  arc 
does  not  become  large.  If  the  lamp  is  not  connected  to 
other  apparatus,  the  pressure  amounts  to  several  milli- 
meters, and  with  quartz  tubes  where  large  currents  are  used 
the  pressure  may  become  even  more  than  one  atmosphere. 

Again  the  pressure  depends  to  a  great  extent  on  such 
things  as  the  size  of  the  tube,  the  condensing  chambers 
and  the  rate  at  which  heat  is  taken  from  the  tube.  The 
hotter  the  tube  becomes,  the  more  mercury  will  be  vapor- 
ized and  the  greater  the  pressure  of  the  vapor.  There  will, 
therefore,  be  a  great  difference  between  a  tube  which  is 
placed  in  water  kept  at  a  constant  temperature  and  a  tube 
surrounded  by  air.  Even  a  difference  in  the  thickness  of 
the  walls  of  a  tube  may  easily  affect  the  rate  at  which  heat 
is  radiated  and  consequently  the  pressure  of  the  vapor,  and 
the  size  of  the  tube  may  not  only  affect  the  pressure  by 
giving  more  room  for  the  vapor,  but  may  affect  it  indirectly 
by  giving  more  chance  for  the  heat  to  escape. 

Moreover  it  is  not  easy  to  make  accurate  determinations 
of  this  pressure  when  it  is  low.  One  can  not  use  any 
arrangement  similar  to  a  McLeod  gauge,  since  the  vapor 
condenses  to  a  liquid  as  soon  as  it  is  taken  from  the  lumi- 


THE  MERCURY  ARC  95 

nous  column.  With  pressures  greater  than  one  millimeter 
fairly  accurate  measurements  can  be  made  by  reading  the 
difference  in  level  between  the  two  arms  of  a  manometer, 
but  with  pressures  less  than  this  such  readings  have  serious 
errors  and  these  lower  pressures  are  important  ones  in 
forming  a  theory  of  the  arc. 

Wills  used  the  following  indirect  method  of  finding  the 
vapor  pressure.  The  temperature  was  first  determined  by 
the  method  already  described  and  from  this,  by  using  tables 
which  give  the  relation  between  the  pressure  of  mercury 
vapor  and  its  temperature,  the  pressure  was  computed. 
This  assumed  that  the  thermojunction  gave  the  correct 
value  of  the  temperature  and  also  that  the  pressure  in  the 
arc  is  the  same  as  it  would  be,  if  the  vapor  and  the  liquid 
in  contact  with  it  were  at  the  same  temperature,  which  is 
the  condition  present  when  measurements  are  made  on 
vapor  pressure.  The  first  of  these  assumptions  has  already 
been  criticized  and  the  second  is  certainly  incorrect. 
There  can  be  no  question  but  that  the  vapor  through 
which  the  current  is  passing  is  very  much  hotter  than  the 
liquid,  which  is  only  a  little  warmer  than  the  surrounding 
air. 

However,  some  idea  of  the  relation  between  voltage  and 
current  can  be  had  from  the  curve  given  by  Cooper  Hewitt,1 
which  is  shown  in  Fig.  28.  The  circles  on  the  continuous 
curve  indicate  the  final  voltages  between  the  terminals  of  a 
mercury  lamp  with  different  currents.  The  crosses  indicate 
readings  which  were  taken  immediately  after  the  current 
had  been  increased  and  before  the  pressure  of  the  gas  had 
changed  to  any  great  extent.  Thus  the  cross  at  a  indicates 
the  reading  when  the  current  had  suddenly  been  increased 

1  Elec.  World,  37,  679;    1901. 


THE  ELECTRIC  ARC 


110 

/ 

"1  00 

/ 

\ 

^10 

&/ 

\ 
\ 

O80 

/\ 

70 

1 

_) 

a 

60 

A 

50 

^ 

-ir 

3         4         5         67 
CURRENT  IN  AMPERES 
FlG.    28. 


from  4.8  amperes  to  6.1  amperes.  As  the  pressure  of  the 
gas  increased  the  current  gradually  decreased  and  the 
voltage  increased,  until  finally  the  point  b  was  reached. 

The  dotted  line  in  this 
figure  indicates  that  the 
voltage  is  very  nearly  con- 
stant when  there  is  no 
change  in  the  density  of 
the  vapor,  even  when  large 
changes  are  made  in  the 
current.  This  probably 
comes  very  near  to  the  true 
relation  between  the  voltage 
of  the  mercury  arc  and  the 
current  with  constant  pres- 
sure. 

The  very  great  increase  in  the  voltage  required  with 
increased  vapor  pressure  of  the  mercury  arc  in  quartz  tubes 
will  be  shown  in  a  following  paragraph. 

The  Cathode  Drop  of  the  Mercury  Arc.  —  In  a  similar 
way  we  find  it  difficult  to  determine  just  what  the  drop  in 
potential  in  different  parts  of  the  arc  really  is.  Thus  Arons 
found  the  cathode  drop  to  be  5.4  volts.  Wills  found  it  to 
be  approximately  5  volts  and  Pollak  gives  it  as  slightly 
more  than  this.  Knipp1  measured  the  drop  in  potential 
between  a  platinum  exploring  wire  and  a  mercury  cathode 
when  the  current  was  3  amperes  and  found  the  cathode 
drop  to  vary  from  6  volts  when  the  pressure  of  the  gas  in 
the  pump  connected  to  the  lamp  was  0.083  mm- to  6.8  volts 
when  the  pressure  was  1.9  mm. 

Stark,  Retschinsky  and  Schaposchnikoff 2  used  mercury 

1  Phys.  Rev.,  31,  106;   1910.          2  Ann.  d.  Phys.,  18,  243;   1905. 


THE  MERCURY  ARC  97 

for  the  exploring  electrode,  so  that  no  potential  difference 
was  introduced  by  using  a  different  metal  from  that  of  the 
cathode.  They  found  the  cathode  drop  to  be  5.27=t  0.09 
volts  and  stated  that  it  is  independent  of  the  current. 

The  Anode  Drop  of  the  Mercury  Arc.  —  The  anode 
drop  has  two  distinct  values;  the  first  when  the  anode 
is  in  the  direct  path  of  the  cathode  rays,  that  is,  when  it 
is  not  covered  by  any  glow,  or  " anode  layer"  as  it  has  been 
called  by  Stark;  the  second  value  occurs  when  there  is  this 
glow.  In  the  first  case  Stark,  Retschinsky  and  Schapo- 
schnikoff,  using  an  iron  anode,  found  the  anode  drop  to 
vary  from  3.14  volts  with  a  current  of  3.6  amperes  to  3.65 
volts  with  one  of  9.3  amperes. 

In  the  second  case  the  anode  drop  would  appear  to  be  in 
the  neighborhood  of  5  volts.  Arons  found  it  to  be  7.4  volts. 
Wills  found  it  to  be  6.5  volts  with  a  current  of  1.25  amperes, 
decreasing  to  4.6  volts  with  one  of  3.25  amperes.  These 
measurements  were  made  with  an  exploring  wire  i  cm. 
from  an  iron  anode.  Pollak1  found  the  value  6  mm.  from 
the  anode  to  be  5.7  volts  when  the  current  was  6.7  amperes. 
Knipp  measured  the  drop  in  potential  between  a  platinum 
anode  and  a  platinum  exploring  wire  when  the  current  was 
3  amperes  and  found  the  anode  drop  to  vary  from  3.6  volts 
when  the  pressure  of  the  gas  in  the  apparatus  connected 
with  the  tube  was  0.083  mm-  to  5.4  volts  when  the  pressure 
was  3  mm.2 

The  Electric  Force  in  the  Mercury  Arc.  —  The  electric 
force  required  to  send  a  current  through  the  vapor  of  a 
mercury  arc  is  surprisingly  small.  Ordinarily  the  resist- 
ance of  a  column  of  gas  is  very  high,  even  when  there  is  a 

1  Ann.  d.  Phys.,  19,  217;   1906. 

2  See  also  Phys.  Rev.,  30,  319;   1910. 


98  THE   ELECTRIC  ARC 

large  amount  of  ionization.  Even  with  a  carbon  arc  in 
air  the  resistance  of  the  gaseous  part  with  a  current  of  six 
amperes  is  approximately  5.5  ohms  per  centimeter.  In  an 
experiment  by  Knipp  when  the  tube  containing  the  mer- 
cury arc  was  22.4  cm.  long  and  3.4  cm.  in  diameter  and 
the  current  was  3  amperes,  the  resistance  was  as  low  as 
0.13  ohm  per  centimeter.  With  larger  currents  it  is  even 
less. 

The  electric  force  in  the  mercury  arc  depends  on  the 
pressure  of  the  vapor,  the  diameter  of  the  tube,  the  amount 
of  current  and  the  temperature.  As  the  pressure  is  in- 
creased there  is  a  decided  increase  in  the  electric  force 
required.  When  working  with  the  tube  mentioned  above 
Knipp  found  the  electric  force  to  vary  from  0.39  volt  per 
centimeter,  when  the  pressure  of  the  gas  in  the  pump  con- 
nected with  the  tube  was  0.083  mm.  to  0.78  volt  per  centi- 
meter when  the  pressure  was  3.0  mm.  The  work  of  Wills 
is  quite  in  agreement  with  these  data. 

Wills  found  that  the  larger  the  tube  the  smaller  the 
electric  force  required.  For  example,  the  electric  force 
with  a  current  of  2  amperes  and  a  pressure  of  i  mm.  varied 
from  0.98  volt  per  centimeter  when  the  diameter  of  the 
tube  was  i  cm.  to  0.37  volt  per  centimeter  when  the 
diameter  was  8  cm.  Arons  also  found  the  force  to  be 
greater  with  smaller  tubes. 

The  electric  force  decreases  as  the  current  is  increased, 
if  the  pressure  of  the  mercury  vapor  remains  constant.  In 
some  data  which  I  hope  soon  to  publish,  it  is  shown  that 
doubling  the  current  causes  the  electric  force  to  decrease 
about  10  per  cent. 

Pollak1  measured  the  potential  through  an  arc  when  the 

1  Ann.  d.  Phys.,  19,  239;   1906. 


THE   MERCURY  ARC  ,        Qp 

current  was  6.7  amperes  and  the  pressure  of  the  vapor 
was  1.33  mm.  This  is  shown  in  Fig.  29.  The  total 
potential  difference  was  22.5  volts.  It  is  of  interest  to 
note  that  there  is  a  point  near  the  anode  where  the 
electric  force  is  in  the  opposite  direction  to  that  in  which 
the  current  is  flowing.  This  is  no  doubt  due  to  an  accu- 


CATHODE 

8 

12t 

c 

20 
?4 

^ 

^ 

^ 

^ 

^ 

^ 

r- 

^^^ 

300    250    200     150    100     50 

DISTANCE  FROM  ANODE 
FIG.  29. 

mulation,  in  this  neighborhood,  of  ions  whose  electrostatic 
effect  is  sufficient  to  reverse  the  original  direction  of  the 
electric  force.  This  accumulation  is  due  to  the  momen- 
tum of  the  ions  which  carries  them  for  a  short  distance 
against  the  electric  force.1 

The  vapor  of  the  mercury  arc  remains  highly  conducting 
and  quite  luminous  even  after  it  has  passed  from  the  arc 
into  a  condensing  chamber.  Stark2  found  that  if  this  vapor 
is  passed  through  a  magnetic  field,  an  E.M.F.  is  induced, 
which  is  perpendicular  to  the  field  and  to  the  direction  of 
the  motion  of  the  vapor.  The  magnitude  of  this  E.M.F. 
indicates  a  velocity  of  the  vapor  of  approximately  280 
meters  per  second. 

1  Phil.  Mag.,  (6),  18,  442;   1909. 

2  Phys.  ZS.,  4,  440;   1903. 


100  THE  ELECTRIC  ARC 

In  some  work  by  myself 1  it  was  shown  that  the  front  of 
this  luminous  region  where  the  mercury  is  condensing  to 
the  liquid  form  has  the  greatest  conductivity  and  the 
greatest  luminosity.  It  was  also  shown  that  this  conduc- 
tivity is  not  due  to  any  rays  sent  out  from  the  arc  itself. 

Mercury  Arc  in  Quartz  Tubes.  —  The  light  efficiency  of 
mercury  vapor  lamps  is  higher  with  large  currents,  but 
tubes  made  of  ordinary  glass  will  melt  when  such  currents 
are  used.  To  avoid  this  difficulty  lamps  are  now  being 
made  of  fused  quartz.  These  lamps  are  among  the  very 
best  as  far  as  watts  per  candle  power  are  concerned.  They 
also  give  off  a  great  amount  of  ultra-violet  light,  which  is 
advantageous  for  photographic  work,  and  because  of  these 
rays  they  can  be  used  for  sterilizing  water. 

The  light  from  such  lamps  appears  to  the  eye  whiter 
than  that  from  the  common  mercury  vapor  lamps  and  yet  it 
is  lacking  in  certain  important  parts  of  the  spectrum  and 
has  the  added  disadvantage  that  the  ultra-violet  rays  are 
very  injurious  to  the  eyes.  However,  these  rays  may  be 
screened  off  by  common  glass,  there  being  sufficient  pro- 
tection, if  the  quartz  lamp  is  placed  inside  a  glass  globe. 
It  is  also  claimed  that  the  rays  are  absorbed  by  a  few  feet 
of  air,  so  that  lamps  placed  fifteen  or  twenty  feet  above  a 
sidewalk  would  not  be  injurious  to  passers-by,  even  if  the 
glass  globe  should  be  broken. 

The  relation  between  current,  potential  difference  and 
the  pressure  of  the  mercury  vapor  in  such  lamps  has  been 
examined  by  Kuch  and  Retschinsky.2  As  the  tube  was 
allowed  to  become  hot  the  vapor  pressure  rose  and  a  larger 
potential  difference  was  necessary  in  order  to  maintain 

1  Phys.  Rev.,  22,  221;   1906. 

2  Ann.  d.  Phys.,  20,  563;  1906. 


THE 


the  arc,  although  it  did  not  increase  as  rapidly  as  the  pres- 
sure. The  following  is  an  abridgement  of  the  table  given 
by  them. 


Potential 
difference. 

Current. 

Pressure  in  cm. 

36 

2.78 

0.2 

67 

4.20 

9.0 

114 

4.50 

29.5 

154 

4.80 

58.7 

202 

4.80 

100.5 

237 

4.50 

138.0 

249 

4.40 

150.0 

Kuch  and  Retschinsky  also  examined  the  temperature 
in  quartz  lamps  using  a  thermo junction.1  They  found 
that  at  the  middle  of  the  tube  the  temperature  became  as 
high  as  1710°  C.,  which  was  the  highest  that  their  thermo- 
junction  would  register.  The  temperature  at  the  sides  was 
at  all  times  lower  than  that  in  the  middle. 

Velocity  of  the  Ions  in  the  Mercury  Arc.  —  The 
velocity  of  the  negative  ions  in  the  mercury  arc  is  much 
greater  than  that  of  the  positive  ones.2  This  has  been 
shown  by  placing  two  secondary  electrodes  in  the  con- 
ducting vapor  of  this  arc  and  passing  a  current  between 
them.  On  examining  the  potential  between  these  elec- 
trodes, it  is  found  that  the  drop  in  potential  near  the  posi- 
tive is  many  times  greater  than  that  near  the  negative. 
As  will  be  shown  in  the  discussion  of  the  theory  of  electrical 
discharge,  this  shows  that  the  negative  ions  have  the 
greater  velocity. 

The  same  thing  is  shown  by  the  work  of  Schenkel3  on  the 

1  Ann.  d.  Phys.,  22,  595;    1907. 

2  Stark,  Retschinsky  and  Schaposchnikoff,  Ann.  d.  Phys.,  18,  230;  1905. 

3  Mitt.  d.  Phys.  Ges.  Zurich,  p.  13,  1906. 


^ELECTRIC   ARC 

Hall  effect  in  the  mercury  arc.  He  states  that  (fe  -  ki)  p 
is  1.42  X  io7  cm.  per  second  per  volt,  where  ki  is  the 
velocity  of  the  positive  ions,  ki  that  of  the  negative  ions 
and  p  the  pressure  of  the  gas  measured  in  millimeters. 

Modifications  of  the  Arc  to  Produce  White  Light.  —  The 
absence  of  some  of  the  colors  in  the  mercury  arc  is  an  ob- 
jection to  its  use  and  many  attempts  have  been  made  to 
supply  the  missing  colors  by  introducing  other  substances 
with  the  mercury.  For  this  purpose  amalgams  of  mercury 
have  been  tried,  but  none  of  them  have  proven  altogether 
successful.  With  the  currents  and  temperatures  com- 
monly used  the  substance  amalgamated  with  the  mercury 
takes  little  or  no  part  in  the  passage  of  the  current.  This 
probably  is  due  to  the  mercury  alone  being  vaporized. 

Several  amalgams  were  tried  by  Arons  who  found  that 
the  potential  difference  was  even  less  with  sodium  and 
potassium  amalgams  than  with  pure  mercury.  With  a 
potassium  amalgam  only  io  volts  were  needed  to  maintain 
a  current  varying  from  3  to  6  amperes.  But  unfortunately 
these  lamps  give  less  light  than  the  common  mercury  vapor 
lamp. 

When  the  tube  was  cooled  by  being  placed  in  the  water 
bath  no  potassium  lines  appeared  in  the  spectrum  of  the 
arc,  even  though  twenty  amperes  of  current  were  used. 
When  the  lamp  was  not  cooled  the  potassium  lines  were 
apparent  with  five  or  more  amperes. 

With  silver  amalgams  the  potential  difference  was  some- 
what larger  than  with  pure  mercury.  The  spectrum  of 
the  silver  appeared  only  at  the  cathode  and  then  only  one 
line,  except  when  the  lamp  was  run  for  a  long  time.  In 
that  case  this  line  disappeared  and  two  others  of  the  silver 
spectrum  appeared  in  its  place.  There  was  excessive  heat- 


THE  MERCURY  ARC  103 

ing  when  a  zinc  amalgam  was  placed  in  the  tube  or  pieces 
of  aluminum  were  allowed  to  float  on  the  mercury.  With 
both  tin  and  aluminum  amalgams  the  potential  difference 
was  much  higher  than  with  pure  mercury. 

More  successful  results  were  attained  by  Gehrke  and 
Baeyer1  who  found  that  an  amalgam  of  100  parts,  by  weight, 
of  zinc  and  30  parts  of  mercury  gives  a  much  better  light 
than  mercury  alone.  Still  better  results  have  been  secured 
when  using  amalgams  in  quartz  tubes,  since  these  tubes 
can  stand  a  higher  temperature  and  are  not  acted  on  chemi- 
cally. Arons2  recommends  the  following  for  use  in  quartz 
tubes:  mercury  59  per  cent,  lead  20  per  cent,  bismuth 
20  per  cent,  zinc  0.5  per  cent  and  cadmium  0.5  per  cent. 

Quite  a  different  method  of  supplying  the  deficient  light 
has  been  suggested  by  Cooper  Hewitt.3  This  is  to  use  a 
reflector  on  whose  surface  are  crystals  which  emit  red 
light  when  illuminated  by  ultra-violet  rays.  No  data  have 
as  yet  been  published  concerning  the  amount  of  red  light 
which  is  thus  obtained  and  it  does  not  seem  to  have  met 
with  any  commercial  success. 

Another  device  and  one  which  promises  excellent  results 
is  a  lamp  described  by  Urbain,  Seal  and  Feige.4  In  this 
the  anode  is  tungsten  and  the  density  of  the  current  is  such 
that  this  is  raised  to  a  very  high  temperature  and  gives  out 
the  greater  part  of  the  light.  This  must  be  in  a  vacuum 
or  in  an  inert  gas,  since  a  trace  of  oxygen  is  sufficient  to 
blacken  the  surrounding  globe.  The  principal  use  of  the 
mercury  is  to  start  the  arc,  it  being  difficult  to  start  an  arc 

1  Elektrot.  ZS.,  27,  383;  1906. 

2  Lond.  Elec.,  62,  387;  1908. 

3  Elec.  World,  56,  1343;  1910. 

4  L'Industrie  Elec.,  March  10,  1911. 


104  THE   ELECTRIC  ARC 

in  an  air-tight  globe  by  other  means.  The  length  of  the 
column  of  luminous  mercury  vapor  is  only  a  few  millimeters. 
The  color  is  bluish  white,  very  similar  to  sunlight,  and 
it  is  said  to  require  but  0.45  watt  per  candle.  It  operates 
on  a  potential  difference  as  low  as  12  volts.  The  voltage 
and  candle  power  may  be  made  greater  by  having  an  inert 
gas  in  the  tube. 

The  lack  of  red  in  the  mercury  arc  is  occasionally  reme- 
died by  combining  the  arc  with  a  tungsten  incandescent 
lamp.  It  is  usually  necessary  to  have  some  resistance  in 
series  with  the  arc.  The  tungsten  lamp  furnishes  this 
resistance  and  at  the  same  time  serves  the  useful  purpose 
of  giving  the  lacking  colors,  thus  making  an  efficient  com- 
bination. 


CHAPTER  VI. 
ALTERNATING-CURRENT  ARCS. 

THE  preceding  discussion  has  been  on  arcs  produced  by 
direct  currents.  These  are  more  efficient  than  alternating- 
current  arcs  and  would  probably  be  used  in  every  case,  if 
it  were  always  convenient  to  have  direct  currents.  Since 
it  is  not,  alternating-current  arcs  have  a  somewhat  limited 
use.  The  differences  between  the  two  kinds  of  arcs  are  in 
general  such  as  might  well  be  expected.  There  is,  however, 
very  great  difficulty  in  maintaining  alternating-current  arcs 
between  metals,  as  will  be  shown  later. 

Alternating-current  Arc  between  Carbon  Terminals.  - 
With  carbon  terminals  the  appearance  of  the  alternating- 
current  arc  is  much  the  same  as  that  of  the  direct-current 
arc,  except  that  the  two  electrodes  appear  alike  in  the  former 
case.  This,  of  course,  is  due  to  the  rapid  change  of  polarity 
of  the  terminals.  However,  with  the  frequencies  commonly 
used,  the  light  appears  to  the  eye  to  be  continuous,  but  it  is 
easy  to  show  with  a  revolving  mirror  that  the  luminosity 
of  the  region  between  the  carbons  fluctuates  greatly,  the 
vapor  being  comparatively  non-luminous  for  a  short  period 
between  each  alternation.1  The  carbons  remain  luminous, 
although  they  also  pass  through  quite  appreciable  changes 
with  each  alternation. 

This  arc  is  accompanied  by  a  humming  sound  corre- 
sponding to  the  frequency  of  alternations.  In  general,  this 

1  Lum.  Elec.,  42,  551  and  618;    1891. 
105 


106  THE   ELECTRIC  ARC 

humming  is  so  loud  as  to  make  the  arc  disagreeable  when 
in  a  closed  room.  It  is  more  noticeable  with  solid  than 
with  cored  carbons. 

The  possibility  of  having  an  alternating-current  arc  is 
due  to  the  fact  that  the  region  between  the  carbons  remains 
conducting  for  an  appreciable  length  of  time  after  the 
current  has  ceased  to  flow.  This  fact  was  known  as  early 
as  1867  when  Le  Roux1  found  that  he  could  start  an  arc 
0.04  sec.  after  the  removal  of  the  E.M.F. 

Characteristic  Curves.  —  Characteristic  curves  for  alter- 
nating-current arcs  show  the  same  general  shape  as  those 
for  direct-current  arcs.  With  both  the  voltage  becomes 
greater  as  the  length  of  the  arc  is  increased  and  less  as  the 
current  is  made  greater.  However,  the  mean  voltage  of 
the  alternating-current  arc  is  less  than  that  for  the  direct- 
current  arc  of  the  same  length  and  current.  Heubach2 
gives  the  equation  E  =  20.4  -f-  i.8/  for  the  alternating- 
current  arc  between  cored  carbons,  when  the  current  is  6.5 
amperes  and  E  =  19.78  +  2.2  /,  when  the  current  is  4.4 
amperes.  As  usual,  E  is  measured  in  volts  and  /  in  milli- 
meters. This  gives,  for  example,  a  voltage  of  29.4  volts  for 
an  arc  5  mm.  long  having  a  current  of  6.5  amperes,  as 
compared  with  55  volts,  the  value  given  by  Mrs.  Ayrton 
for  a  direct-current  arc  having  the  same  current  and  length 
between  a  cored  anode  and  a  solid  cathode.  The  fact  that 
both  of  the  carbons  were  cored  in  the  alternating-current 
arc  no  doubt  explains  part  of  the  difference,  but  only  a 
small  part.  In  some  observations  made  by  myself  in  using 
cored  carbons  for  both  alternating-  and  direct- current  arcs 
it  was  found  that  the  voltage  for  the  former  was  from 

1  C.  R.,  65, 1149;  1867. 

2  Elektrot.  ZS.,  13,  460;  1892. 


ALTERNATING-CURRENT  ARCS  107 

15  to  20  volts  lower  than  that  for  the  latter,  the  current  and 
length  of  arcs  being  the  same  in  both  cases. 

The  characteristic  curves  for  the  flaming  arc  with  alter- 
nating current  are  nearly  identical  with  those  for  the  same 
arc  with  direct  current.  One  curve  taken  by  myself  for 
a  flaming  arc  10  mm.  long  with  alternating  current  was 
identical  throughout  the  greater  part  of  its  length  with 
that  taken  with  the  same  carbons  and  length  where  a 
direct  current  was  used,  as  shown  in  Fig.  16. 

Current  and  Potential  Difference  at  Different  Phases.  — 
As  far  as  I  have  been  able  to  learn  the  first  published  work 
on  the  alternating-current  arc  was  by  Joubert,  in  iSSo,1 
who  showed  the  values  of  the  potential  difference  and  the 
current  at  different  phases  of  the  alternations.  His  method 
was  the  one  which  is  well  known  in  the  work  on  alternating 
currents,  where  a  measuring  instrument  is  connected  to 
the  circuit  for  a  brief  length  of  time  during  each  alternation, 
the  connection  being  always  made  at  the  same  phase  of 
the  alternation.  He  found  the  curve  for  the  current  to  be 
nearly  a  sine  curve,  while  that  for  the  potential  difference 
was  greatly  deformed.  This  observation  was  confirmed 
by  Tobey  and  Walbridge.2  The  form  of  these  curves  has 
been  found  to  vary  with  the  kind  of  dynamo  used,  the 
character  of  the  carbon  and  the  length  of  the  arc.3 

The  preceding  method  gave  the  average  value  of  some 

1  C.  R.,  91,  161;    1880. 

2  Amer.  Inst.  Elec.  Eng.,  7,  367;   1890. 

3  Rossler  and  Wedding,  Elektrot.  ZS.,  15,  315;   1894. 
Fleming  and  Petavel,  Phil.  Mag.,  (5),  41,  315;    1896. 
Frith,  Phil.  Mag.,  (5),  41,  507;  1896. 

C.  S.  Smith,  Lond.  Elec.,  39,  855;  1897. 

Beckit  Burnie,  Lond.  Elec.,  39,  849;  1897. 

Eichberg  and  Kallir,  Wien.  Sitzungbr.,  107,  2 A,  658;   1898. 


108  THE   ELECTRIC  ARC 

particular  phase  of  the  current  or  potential  difference 
during  many  periods.  The  oscillograph  devised  by  Blon- 
del1  gives  a  photograph  of  these  curves  during  the  whole 
of  some  one  period.  This  instrument  is  in  principle  a 
galvanometer,  the  period  of  whose  needle  is  very  short,  so 
that  the  mirror  is  able  to  follow  closely  each  fluctuation 
of  the  current.  A  spot  of  light  may  be  reflected  from  this 


FIG.  30. 

mirror  to  a  rapidly  moving  photographic  film  which  records 
the  changes  in  the  current.  One  such  device  may  be  put 
in  series  with  the  arc  and  another  in  shunt  with  it,  so  that 
records  of  the  current  and  voltage  may  be  made  on  the 
same  film  and  compared  at  each  phase  of  the  alternation, 
as  in  Fig.  30. 2 

It  will  be  seen  from  this  that  the  current  does  not 
at  first  increase  rapidly,  while  the  voltage  reaches  its 
highest  value  in  a  small  fraction  of  a  cycle.  This  is  due 

1  C.  R.,  127,  1019;   1898. 

2  An  improvement  in  this  instrument  was  made  by  Duddell  and  Mar- 
chant  (Journ.  Ins.  Elec.  Eng.,  28,  i;  1899)  and  a  very  complete  set  of 
curves  with  different  kinds  of  carbons,  period  of  alternation,  currents  and 
lengths  of  arc  were  given  by  them. 


ALTERNATING-CURRENT  ARCS  1 09 

to  the  fact  that  a  potential  difference  of  several  volts  is 
necessary  in  order  to  produce  any  current  at  all  through 
the  arc. 

As  the  current  increases  the  voltage  decreases  slightly, 
since  it  requires  less  voltage  to  maintain  a  large  current 
than  a  small  one.  The  amount  of  the  current  during  this 
part  of  the  cycle  is  determined  chiefly  by  the  resistance 
and  inductance  in  the  other  parts  of  the  circuit.  Near  the 
end  of  the  phase  the  current  rapidly  approaches  zero,  since 

the  voltage  has  then  become  less   

than  that  needed  to  maintain  an 

arc.  &->|    / 

There  is  given  in  Fig.  3 1  a  curve   I 
taken  with  an  oscillograph  where 
the  voltage  curve  aa'  is  given  in 
a  negative  direction  in  order  that       / 
it  may  not  be  confused  with  the   j£/     a-  \J_  J      J 

current  curve  bbr .     These  curves  _ 

FIG.  31. 

were   taken  by  Simon1  with   an 

arc  between  solid  carbons  5  mm.  in  diameter  placed 
horizontally  above  a  Bunsen  burner,  so  that  the  arc  was 
in  the  flame  of  the  burner.  The  arc  was  2.5  mm.  in  length 
and  the  current  was  2.3  amperes  with  a  frequency  of  50 
per  second. 

The  flaming  arcs  behave  with  alternating  currents  much 
the  same  as  the  arc  between  cored  carbons,  although  the 
curves  of  the  flaming  arc  taken  with  an  oscillograph  were 
more  similar  to  those  of  the  solid  than  to  those  of  the  cored 
carbon  arcs.2  Fig.  32  gives  such  curves  when  there  was 
non-inductive  resistance  in  series  with  the  arc. 

1  Phys.  ZS.,  6,  305;    1905. 

2  Blondel,  Trans.  Intern.  Elec.  Cong.,  2,  744;    1904. 


no 


THE  ELECTRIC  ARC 


FIG.  32. 

Dynamical  Characteristic  Curves.  —  Mention  has  al- 
ready been  made  of  what  were  called  " dynamical"  charac- 
teristic curves.  Such  curves  show  the  relation  between 
the  potential  difference  and  the  current  for  arcs  which  are 


J_ 


CURRENT  IN  AMPERES 


FIG.  33. 


ALTERNATING-CURRENT  ARCS 


III 


rapidly  changing.  Thus,  if  the  different  values  of  the 
current  as  shown  in  Fig.  31  are  taken  as  abscissae  and  the 
corresponding  values  of  the  potential  difference  as  ordinates, 
one  would  have  the  curve  given  in  Fig.  33,  which  is  a 
dynamical  characteristic  curve. 

This  "gives  in  a  different  way  some  of  the  things  shown 
by  Fig.  30  and  also  calls  attention  to  the  fact  that  the 
relation  between  potential  difference  and  current  is  not  the 
same  when  the  current  is  increasing  as  when  it  is  decreasing. 
Thus  the  part  of  the  curve  at  the  left  indicates  the 
relation  existing  when  the  current  is  changing  from  the 
greatest  negative  current  to  the  maximum  positive.  The 
curve  on  the  right  indicates  the  relation 
when  the  current  is  changing  from  posi- 
tive to  negative. 

When  the  current  is  increasing,  the 
carbons  are  not  so  hot  as  they  are  when 
it  has  been  large  and  is  becoming  small. 
With  the  cooler  electrodes  the  potential 
difference  is  greater  than  when  the 
electrodes  are  hotter,  although  the  cur- 
rent is  the  same.  This  peculiarity  of 
the  curves  is  called  by  Simon  "  arc-light 
hysteresis." 

These  curves  are  quite  different  from 
those  shown  in  Figs.  3-7.  There  the 
potential  difference  approached  infinity 
as  the  current  approached  zero.  Here 
the  two  approach  zero  together.  The 
reason  is  that  the  part  of  the  curve 
near  the  origin  does  not  strictly 
refer  to  an  arc.  It  refers  rather  to  the  simpler  form  of 


112  THE  ELECTRIC  ARC 

discharge  between  two  hot  bodies  where  there  is  no 
ionization  by  impact  at  the  surface  of  the  electrode, 
as,  for  example,  the  discharge  from  a  hot  piece  of  iron  or 
platinum. 

With  this  simpler  form  of  discharge  the  current  will  be- 
come smaller  as  the  voltage  becomes  smaller.  The  two 
do  not  necessarily  approach  zero  at  the  same  time,  since 
there  may  be  a  small  E.M.F.  due  to  the  difference  in  tem- 
perature between  the  two  bodies  and  since  it  takes  an 
appreciable  time  for  the  ions  to  move  across  the  gap.  But 
the  characteristic  curve  for  such  a  discharge  would  at  least 
go  near  the  origin,  as  do  the  curves  in  Fig.  33.1 

Fall  of  Potential  in  Alternating-current  Arc.  —  The  fall 
of  potential  in  different  parts  of  the  alternating-current  arc 

rCurrent  „  ^Pd.  between   cd 

-Pd.  between   a  b 
-Pd.  between   b  C 


FIG.  35. 

was  examined  by  Duddell  and  Marchant.  Their  results 
are  shown  in  Fig.  35.  Fig.  34  shows  the  position  of  the 
exploring  carbons.  The  left  hand  part  of  Fig.  35  shows  the 
curves  of  current  and  total  potential  difference,  while  the 
part  on  the  right  shows  the  potential  difference  in  different 
parts  of  the  arc.  All  the  curves  of  potential  difference  show 
the  same  general  shape.  The  carbons  used  were  "Apostle" 
carbons  13  mm.  in  diameter.  The  arc  was  6  mm.  long 

1  A  very  complete  study  of  dynamic  characteristic  curves  with  the  arc 
in  various  gases  and  in  air  at  reduced  pressures  has  been  given  by  Gertrude 
Lange  (Ann.  d.  Phys.,  32,  589;  1910). 


ALTERNATING-CURRENT   ARCS 


and  there  were  14.8  amperes  and  97  alternations  per 
second. 

Phase  Difference  in  the  Alternating-current  Arc.  —  As 
was  shown  in  Fig.  30  the  current  lags  somewhat  behind 
the  potential  difference.  As  a  result  the  power  given  to 
the  arc  is  not  equal  to  the  product  of  the  current  as 
measured  by  an  alternating-current  ammeter  times  the  volt- 
age as  measured  by  a  voltmeter.  In  this  respect  the  arc 
behaves  as  a  resistance  having  self-induction.  The  phe- 
nomenon, however,  is  not  due  to  self-induction,  but  to  the 
fact  that  the  conductivity  between  the  carbons  is  not  so 
good  when  the  arc  has  momentarily  been  extinguished  and 
the  gas  and  electrodes  have  become  cooled  as  when  the  cur- 
rent has  been  flowing. 

The  existence  of  this  apparent  phase  difference  was 
pointed  out  by  Heubach1  who  found  it  to  exist  for  solid 
carbons  but  not  for  cored  carbons.  In  the  following  table 
the  value  for  c,  the  power  factor,  is  given  for  different  car- 
bons and  with  different  alternations  per  second.2 


Carbons. 

Alternations 

C. 

per  sec. 

Upper. 

Lower. 

(       127 

0.870 

Solid 

Solid 

1          97 
1          70 

0.865 
0.805 

I         57 

0.750 

{127 

0.975 

Solid 

Cored 

97 
70 

0.965 
0.935 

46 

0.915 

(       127 

0.985 

Cored 

Cored 

1          97 
1         70 

0.980 
0.970 

46 

0.960 

1  Elecktrot.  ZS.,  13,  460;   1892. 

2  Duddell  and  Marchant,  Journ.  Inst.  Elec.  Eng.,  28,  86 ;  1899. 


114  THE  ELECTRIC  ARC 

Alternating-current  Arc  between  Metals.  —  Mention 
was  made  by  Jamin  and  Maneuvier1  in  1882  of  alternating- 
current  arcs  having  a  metal  for  one  terminal  and  carbon 
for  the  other,  but,  curiously,  they  make  no  mention  of  what 
will  occur  when  both  terminals  are  metals.  The  difficulty 
of  maintaining  such  an  arc  was  no  doubt  well  known,  but 
the  first  observation  to  which  I  have  been  able  to  find  a 
reference  was  made  by  Wurts  in  1892.2  He  found  that  he 
could  not  maintain  such  arcs  between  zinc,  cadmium, 
bismuth  or  antimony,  even  with  large  voltages.  These  he 
called  " non-arcing"  metals.  They  are  still  often  called 
this,  although  the  work  of  other  experimenters  would  indi- 
cate that  they  are  no  more  non-arcing  tharr  many  other 
metals. 

Arons3  using  an  E.M.F.  of  360  volts  was  unable  to  main- 
tain such  an  arc  between  mercury,  aluminum,  copper,  iron, 
platinum,  brass  or  nickelin.  He  believed  that  it  would  be 
necessary  to  have  an  E.M.F.  sufficiently  high  to  start  the 
discharge  each  time  with  a  spark. 

Similar  observations  were  made  by  Granqvist4  who  be- 
lieved that  the  difficulty  was  due  to  the  fact  that  the  heat 
is  rapidly  conducted  away  by  the  metal.  Steinmetz5 
states  that  it  is  necessary  to  have  500  volts  in  order  to 
maintain  an  alternating-current  arc  between  magnetite 
terminals  and  then  it  is  very  unsteady  and  the  current 
is  partially  rectified.  In  some  experiments  performed 
by  myself  it  was  found  that  this  form  of  arc  could  not  be 

1  C.  R.,  94,  1615;  1882. 

2  Amer.  Inst.  Elec.  Eng.,  9,  102;  1892. 

3  Wied.  Ann.,  57,  195;  1896. 

4  Upsala  Rom.  Soc.,  p.  i;  1903.   Phys.  ZS.,  4,  537;  1903.   Science  Abs.,  7, 
40;  1904,  and  10,  344;  1907. 

6  Trans.  Intern.  Elec.  Cong.,  St.  Louis,  2,  719;    1904. 


ALTERNATING-CURRENT  ARCS 


maintained  between  iron  and  copper  terminals  either  in 
air  or  in  a  vacuum  with  an  E.M.F.  of  220  volts.1  With 
graphite  it  was  very  difficult  to  maintain  an  arc  with  such 
a  voltage. 

There  appears  to  be  no  further  work  with  such  arcs  where 
the  current  was  comparable  with  that  of  the  common  arc. 
There  have,  however,  been  two  investigations  where  very 
small  currents  and  high  E.M.F.'s  were  used,  but  it  is 
difficult  to  decide  whether  these  should  be  considered  as 
arcs  or  as  sparks. 

The  first  of  these  investigations  was  made  by  Guye  and 
Monash.2  They  concluded  from  their  experiments  that 
the  difficulty  of  obtaining  the  alternating-current  arc  be- 
tween metals  increases  as  the  atomic  weight  of  the  metal 
becomes  greater.  In  the  following  table  there  are  given 
the  potential  differences  with  the  metals  investigated  by 
them  when  the  current  was  0.04  ampere,  the  length 
of  the  arc  5  mm.,  and  the  alternations  47  per  second. 
Accompanying  these  potential  differences  are  the  atomic 
weights. 


Bodies. 

C 

Mg 

Fe 

Ni 

Cu 

Ag 

Cd 

Pt 

Au 

Atomic  Weight  
Potential  Dif  

12 
640 

24 
700 

55-9 
850 

58.6 
850 

63.2 
870 

107.7 
900 

iiS-S 
725 

194-3 

IOOO 

196.7 
1040 

Guye  and  Bron3  found  that  by  using  an  E.M.F.  of  20,000 
volts  and  by  keeping  the  electrodes  at  temperatures  very 
near  their  melting  points  arcs  of  considerable  stability  were 
obtained.  Under  these  conditions  the  period  of  extinction 

1  Phys.  Rev.,  20,  374;   1905. 

2  Eel.  Elec.,  34,  305;   1902.     Elektrot.  ZS.,  23,  956;   1902. 

3  Archives  des  Sciences,  25,  453  and  549;    1908.     C.  R.,  146,  1090;  and 
147,  49;    1908. 


Il6  THE  ELECTRIC  ARC 

was  negligible  and  the  " minimum  potential  difference" 
tended  to  a  constant  value  whatever  the  nature  of  the 
metal,  provided  it  was  not  easily  melted.  This  voltage 
was  in  the  neighborhood  of  475  volts,  the  experiments  being 
performed  in  air  at  a  pressure  of  40  cm.,  the  distance  be- 
tween the  electrodes  being  4  mm.,  the  current  o.i  ampere 
and  the  frequency  50  alternations  per  second. 

The  space  between  the  electrodes  with  an  arc  between 
metals  loses  its  conductivity  more  quickly  than  with  the 
arc  between  carbons.  This  is  shown  by  direct  measure- 
ments of  the  conductivity  and  by  the  difficulty  which  is 
experienced  in  trying  to  maintain  an  alternating-current 
arc  between  metals.  The  experience  of  Edlund  with  the 
arc  between  silver  electrodes  has  already  been  mentioned. 
Arons1  found  that  the  arc  between  metals  lost  its  con- 
ductivity very  quickly.  Duddell2  found  that  it  was  not 
possible  to  restart  an  arc  between  copper  electrodes 
1/27000  sec.  after  it  had  been  broken. 

As  has  been  stated  Guye  and  Monash  believed  that  the 
difficulty  is  proportional  to  the  atomic  weight  of  the  metal, 
but  it  is  hard  to  see  how  the  atomic  weight  can  directly 
affect  the  arc  and  the  evidence  is  not  strong  for  this  view. 
Their  data,  for  example,  do  not  agree  with  the  data  of  those 
who  have  worked  with  larger  currents. 

Granqvist  believes  that  the  difficulty  of  maintaining  such 
an  arc  is  due  to  the  rapid  conduction  of  heat  by  the 
electrodes.  This,  no  doubt,  has  much  to  do  with  the 
phenomenon,  and  yet  it  is  not  a  complete  explanation,  as 
is  shown  by  the  behavior  of  the  alternating- current  arc 
between  carbons  with  different  pressures  of  the  surrounding 

1  Wied.  Ann.,  57,  193;   1896. 

2  Lond.  Elec.,  46,  311;  1900. 


ALTERNATING-CURRENT  ARCS 


gas.  At  atmospheric  pressure  it  is  easy  to  maintain  such 
an  arc  on  a  circuit  of  no  volts.  In  a  vacuum  where  the 
pressure  is  less  than  0.5  mm.  it  is  not  possible  to  do  so.1 
The  atomic  weight  has  not  changed  and  the  heat  conduc- 
tivity has  not  increased,  so  that  neither  of  the  above  ex- 
planations applies  in  this  case. 

All  our  knowledge  of  the  arc  would  indicate  that  we 
must  look  to  the  cathode  for  an  explanation  of  the  difficulty. 
When  this  is  sufficiently  hot  a  current  can  be  started. 
When  it  is  not,  no  current  will  flow.  In  this  case  there 
are  two  things  to  be  considered;  first,  how  much  heat  was 
developed  at  the  cathode  during  the  preceding  part  of 
the  cycle  when  it  was  the  anode,  and  secondly,  how  fast 
it  is  conducted  away.  Granqvist  called  attention  only 
to  the  second  of  these  considerations. 

With  the  carbon  arc  we  not  only  have  electrodes  which 
are  poor  thermal  conductors,  but  we  have  an  exceptionally 
large  anode  drop  with  its  corresponding  large  development 
of  heat  near  the  anode.  The  electrode  reaches  a  high 
temperature  while  being  the  anode,  and  does  not  cool  off 
rapidly  during  the  change  in  the  direction  of  the  current. 
With  the  metal  arc  there  is  less  heat  developed  and  it  is 
conducted  away  more  rapidly. 

With  a  carbon  arc  in  a  vacuum  the  heat  is  not  conducted 
away  more  rapidly  than  with  such  an  arc  in  air,  but  the 
anode  drop  is  here  very  small  and  the  carbon  does  not  rise 
to  a  sufficiently  high  temperature  during  the  time  that  it 
is  the  anode  to  enable  it  to  start  the  arc  when  it  becomes 
the  cathode. 

It  is  altogether  possible  that  with  the  metal  arc  the  ions 
between  the  electrodes  become  more  quickly  loaded  with 

1  Phys.  Rev.,  20,  374;  1905. 


Il8  THE  ELECTRIC  ARC 

condensing  vapor  than  in  the  carbon  arc  and  that  this  may 
hinder  the  starting  of  the  arc,  but  as  yet  we  have  no  direct 
evidence  of  such  action. 

Alternating-current  Arc  between  Unlike  Terminals.  — 
When  an  alternating  current  is  passed  between  two  unlike 
terminals,  the  current  is  in  general  greater  in  one  direction 
than  in  the  other.  This  is  most  noticeable  when  one  ter- 
minal is  a  metal  and  the  other  carbon,  but  it  is  possible 
to  observe  it  even  with  two  carbon  terminals,  if  they  are 
of  different  sizes,  or  if  one  is  cored  and  the  other  solid.1 

Jamin  and  Maneuvier2  seem  to  have  been  the  first  to 
observe  this.  They  found  that  when  two  carbons  are 
of  different  sizes  the  current  from  the  larger  is  greater 
than  that  in  the  opposite  direction.  The  difference  be- 
tween the  two  currents  is  greater  the  greater  the  differ- 
ence in  the  size  of  the  carbons.  They  found  also  that  with 
short  arcs  between  a  metal  and  carbon  there  is  little 
difference  between  the  currents  in  the  two  directions.  The 
excess  is  greatest  when  mercury  is  used  for  one  of  the 
electrodes. 

When  an  alternating-current  arc  is  maintained  between 
a  carbon  rod  and  a  rotating  carbon  with  an  E.M.F.  of 
220  volts  and  50  alternations  per  second  about  30  per  cent 
of  the  energy  is  rectified,  the  rod  being  positive  with  respect 
to  the  carbon.3 

A  large  number  of  photographs  which  showed  the  curves 
of  current  and  potential  difference  with  the  alternating- 

1  Sahulka,  Wien.  Sitzungbr.,  103,  2A,  925;  1894. 
Gold,  Wien.  Sitzungbr.,  104,  2 A,  814;  1895. 
Von  Lang,  Wied.  Ann.,  63,  191;  1897. 

Eichberg  and  Kallir,  Wien.  Sitzungbr.,  107,  2 A,  657;  1898. 

2  C.  R.,  94,  1615;  1882. 

3  Sahulka,  Elektrot.  ZS.,  29,  949;  1908. 


ALTERNATING-CURRENT  ARCS  119 

current  arc  between  carbon  and  a  metal  were  taken  by 
Blondel1  by  means  of  the  oscillograph.  He  found  that 
when  there  was  inductive  resistance  in  the  circuit,  the  arc 
was  extinguished  for  a  longer  time  than  when  there  was 
none.2  Fig.  36  gives  a  good  idea  of  such  curves.  During 


FIG.  36. 

one  half  period  the  current  and  potential  difference  curves 
are  much  the  same  as  with  ordinary  alternating-current 
arcs.  In  the  other  the  voltage  rises  to  its  normal  value, 
but  there  is  no  corresponding  current. 

This  phenomenon  is  the  same  as  that  described  on  page  69 
where  the  peculiarities  of  the  direct-current  arc  between 
unlike  terminals  were  discussed,  and  the  explanation  of  this 
is,  of  course,  the  same  as  that  given  in  that  discussion. 

Alternating-current  Arc  in  Other  Gases  than  Air.  — 
There  have  been  but  few  experiments  performed  on  the 
alternating  current  in  other  gases  than  air.  The  results 
obtained  from  these  are  such  as  one  would  expect  from 
those  on  the  direct-current  arc  in  different  gases.  Thus  it 
has  been  observed  that  it  is  very  difficult  to  maintain  an 

1  C.  R.,  128,  727;  1899. 

2  See  also  Duddell  and  Marchant,  Journ.  Inst.  Elec.  Eng.,  28,  ij   1899. 


120  THE  ELECTRIC  ARC 

alternating-current  arc  in  hydrogen.1  For  example,  Upson 
found  that  he  could  not  maintain  such  an  arc  between 
carbon  terminals  with  a  length  of  more  than  0.03  in.,  the 
E.M.F.  being  100  volts  and  the  frequency  80  per  second. 
Under  similar  conditions  in  coal  gas  an  arc  longer  than 
0.02  in.  could  not  be  maintained. 

Oscillographs  showing  the  current  and  voltage  with 
alternating-current  arcs  in  coal  gas  have  been  obtained  by 
Morris.2  These  show  that  the  voltage  rose  to  370  volts 
before  the  current  commenced. 

Mercury  Arc  Rectifier.  —  As  has  been  stated  it  is  diffi- 
cult to  maintain  an  alternating-current  arc  in  a  vacuum, 
even  when  the  electrodes  are  carbon.  With  any  other 
electrodes  it  appears  to  be  quite  impossible  to  do  so.  The 
difficulty  appears  to  be  due  to  the  fact  that  the  terminal 
which  is  the  anode  during  one  half  period  does  not  become 
hot  enough  during  that  time  to  become  the  cathode  when 
the  E.M.F.  is  reversed,  for  a  terminal  must  be  very  hot 
in  order  to  become  the  cathode  of  an  arc. 

On  the  other  hand  a  terminal  can  easily  become  the 
anode,  even  when  it  is  cold.  Use  has  been  made  of  these 
two  facts  in  devising  an  apparatus  for  rectifying  alternating 
currents.  The  first  device  of  this  sort  was  made  by  Cooper 
Hewitt  and  called  by  him  the  static  converter.  This  form 
can  be  used  only  with  a  three-phase  current.  It  is  shown 
diagrammatically  in  Fig.  37.  The  rectifier  consists  of  a 
tube,  T,  with  one  mercury  electrode  at  the  bottom  and 
three  iron  electrodes  above.  The  iron  electrodes  are  con- 
nected to  the  three  circuits  of  a  star-connected  three-phase 

1  Child,  Phys.  Rev.,  20,  374;  1905. 

Upson,  Lond.  Elec.,  60,  58;   1907.    Phil.  Mag.,  (5),  14,  141;  1907. 

2  Lond.  Elec.,  59,  707;  1907. 


ALTERNATING-CURRENT  ARCS 


121 


generator;  the  mercury  electrode  is  connected  to  the  neutral 
point  of  the  winding.  At  all  times  there  will  be  one  of  the 
iron  electrodes  which  is  positive  as  compared  with  the 
mercury  electrode.  If  an  arc  is  once  started  from  one  of 


these  to  the  mercury,  the  discharge  easily  changes  to  a 
second  electrode  when  that  in  turn  becomes  positive.  On 
the  other  hand  no  discharge  can  pass  to  an  iron  electrode 
at  the  time  it  becomes  negative,  since  it  can  not  become  a 
cathode  after  having  once  ceased  to  be  one.  As  a  result 
the  current  will  at  all  times  be  flowing  from  one  of  the  iron 
electrodes  to  the  mercury  and  will  never  flow  in  the  opposite 
direction,  so  that  between  a  and  b  there  will  be  a  continuous 
direct  current.  This  can  be  used  for  lighting  a  lamp  at  I, 
for  example,  or  in  any  other  way  desired. 

For  starting  the  rectifier  a  fourth  iron  electrode  (not 
shown  in  the  diagram)  was  introduced  and  a  momentary 
high  E.M.F.  was  produced  between  this  and  the  mercury. 

The  drop  in  potential  through  the  rectifier  was  found  by 
Cooper  Hewitt  to  be  about  14  volts.  The  percentage  of 


122 


THE  ELECTRIC   ARC 


' VWWWWWV ' 

Transformer 

f VWWW IG 

A.  C.  Supply  ° 


loss  would,  therefore,  be  rather  large  on  a  no- volt  circuit. 
On  circuits  with  higher  voltage  it  would  be  correspondingly 
smaller. 

An  improved  form  of  the  converter  which  can  be  used 
with  currents  as  large  as  700  amperes  has  recently  been 
brought  out  by  the  same  inventor.1  This  is  made  of  a 
metallic  envelope,  through  which  the  electrodes  are  in- 
serted by  way  of  porcelain  tubes,  the  whole  being  sub- 
jected to  artificial  cooling.  It  has  been  found  possible  to 
use  such  a  tube  for  a  month  without  being  reexhausted 
while  giving  200  kilowatts.  This  may  well  prove  of  value 

as  a  connecting  link  between 
an  alternating-current  supply 
system  and  direct-current 
motors,  such  as  are  largely 
used  in.  railway  service. 

An  ingenious  modification 
of  this  for  use  on  a  single- 
phase  circuit  is  described  by 
Weintraub.2  This  is  shown 
in  Fig.  38.  The  tube  has  three 
terminals,  A,  A'  and  B.  B 
is  a  mercury  terminal.  The 
others  may  be  either  mercury, 
iron  or  carbon.  Those  shown 
in  the  tube  are  carbon.  C  is 
an  auxiliary  terminal  used  in 
starting  the  arc.  A  and  A' 

are  connected  to  the  terminals  of  an  alternating-current 
supply.  E  and  F  are  coils  having  considerable  inductance. 


J© 
' — ^IRRHP — i — IfiRRP — 


FIG.  38. 


1  Elec.  World,  59,  628;  1912. 

2  Phil.  Mag.,  (6),  7,  122;   1904. 


ALTERNATING-CURRENT  ARCS  123 

If  the  tube  is  rocked  so  that  the  mercury  in  B  is  brought 
into  momentary  contact  with  that  in  C  and  then  separated 
an  arc  is  started.  At  the  moment  that  this  occurs  either 
A  or  A'  will  be  positive  with  respect  to  B  and  a  current 
will  flow  from  whichever  is  positive  to  the  cathode  B.  If 
the  auxiliary  arc  is  not  maintained,  the  current  from  A  or 
A'  will  continue  until  A  and  B  are  at  the  same  potential. 
If  there  were  no  self-induction  in  the  circuit  the  arc  would 
then  cease,  but  with  the  inductance  coils  at  E  and  F  the 
arc  will  continue  even  without  the  auxiliary  arc,  as  will  be 
seen  from  the  following. 

Let  us  assume,  for  example,  that  A  is  at  a  higher  potential 
than  B  at  the  moment  contact  is  broken  between  B  and  C. 
Current  will  then  flow  from  A  to  B  down  to  D  and  through 
E  back  to  G.  Only  a  very  small  amount  will  flow  through 
F  because  of  its  large  inductance.  As  soon  as  this  current 
begins  to  decrease  the  energy  stored  in  the  coil  E  raises  A' 
to  a  higher  potential  than  B  and  current  flows  from  A'  to 
B.  This  occurs  while  the  current  from  A  is  decreasing 
but  before  it  has  stopped,  so  that  at  this  moment  current 
is  flowing  to  B  from  both  A  and  A' ',  as  is  indicated  in  the 
diagram  by  the  arrows  without  circles. 

As  the  direction  of  the  E.M.F.  is  reversed  the  current 
will  cease  to  flow  from  A,  but  it  will  continue  to  flow  from 
A'  because  of  the  E.M.F.  induced  by  the  coil  E,  and  before 
this  E.M.F.  has  ceased  the  transformer  will  cause  G  to  be 
positive  and  the  current  will  continue  to  flow  from  A' .  It 
can  not  flow  to  A  because  a  cold  terminal  can  not  become 
the  cathode  of  an  arc.  It  will,  therefore,  flow  through  B 
and  F  and  there  will  be  the  same  sequence  of  events  on 
this  side  as  had  previously  occurred  on  the  other,  the 
current  for  a  brief  interval  flowing  from  both  A'  and  A 


124  THE   ELECTRIC   ARC 

through  B  and  the  inductance  F,  as  indicated  by  the  arrows 
with  circles. 

The  efficiency  of  this  rectifier  is  good  even  on  a  hundred- 
volt  circuit,  and  becomes  higher  as  the  voltage  is  raised. 
Norden1  states  that  the  efficiency  of  such  rectifiers  giving 
100  volts  is  80  per  cent  for  currents  varying  from  10  to 
30  amperes,  while  the  efficiency  of  the  rotary  converter 
giving  the  same  voltage  is  only  54  per  cent  for  10  amperes 
and  62  per  cent  for  30  amperes.  In  general,  he  says,  the 
static  rectifier  is  more  efficient  than  the  rotary  converter 
when  less  than  5  kilowatts  are  being  used. 

The  "return"  current,  that  is,  the  current  passing  through 
the  tube  in  a  direction  opposite  to  the  main  current,  is 
ordinarily  but  a  few  million ths  of  an  ampere.2  It  increases 
slightly  as  the  voltage  is  increased  and  very  greatly  when 
the  current  is  increased,  so  that  the  tube  becomes  hot. 

As  has  been  stated  it  is  not  possible  to  pass  an  alternat- 
ing current  through  a  vacuum  tube  having  mercury  for 
one  of  the  electrodes.  This  is  true  when  there  are  only 
two  electrodes  or  when  there  is  no  inductance  in  the  circuit, 
but  evidently  there  is  no  reason  why  the  mercury  arc  recti- 
fier, as  described  above,  should  not  be  used  to  give  light,  and 
in  fact  such  a  lamp  is  now  being  sold.  When  used  for  this 
purpose  it  is  made  longer  than  when  used  as  a  rectifier  and 
the  voltages  are  so  arranged  that  the  greater  part  of  the 
energy  is  used  in  the  tube  instead  of  in  the  outside  circuit. 
Such  an  arrangement  is  a  mercury  vapor  lamp  for  alter- 
nating circuits. 

It  has  been  found  by  Bedell3  that  partial  rectification 

1  Allgem.  Elek.  Ges.  ZS.,  Feb.,  1910. 

2  Schultze,  Elektrot.  ZS.,  31,  28;  1910. 

3  Elec.  World,  40,  408;  1902. 


ALTERNATING-CURRENT  ARCS  125 

may  be  produced  by  placing  an  alternating-current  arc 
between  carbon  terminals  in  a  magnetic  field.  One  end 
of  the  arc  can  then  be  made  to  alternate  between  two 
terminals  which  are  very  near  each  other  but  not  in  contact. 
As  a  result  one  of  these  terminals  will  receive  nearly  all  of 
the  positive  current  and  the  other  nearly  all  of  the  negative. 
The  terminals  can  then  be  connected  so  as  to  produce  a 
direct  current  through  part  of  the  circuit. 


CHAPTER  VII. 

PHOTOMETRY  OF  THE  ELECTRIC  ARC. 

THE  chief  use  of  the  arc  is  to  give  light  and  its  commercial 
value  depends  on  the  amount  and  color  of  its  light.  These 
subjects  will  be  considered  briefly  in  the  following  chapter, 
but  they  belong  more  properly  to  books  on  photometry  and 
spectroscopy  and  the  reader  is  referred  to  such  books  for 
their  more  adequate  treatment. 

There  are  three  difficulties  met  with  when  making 
measurements  of  the  candle  power  of  electric  lamps.  The 
first  and  most  radical  one  is  due  to  the  difference  between 
the  color  of  the  arc  and  that  of  the  light  standards  in 
common  use.  Nearly  all  other  forms  of  illumination  are 
similar  in  color  to  the  candle  and  can  be  compared  with  it, 
but  this  can  not  be  said  of  the  arc.  The  open  arc  is  dis- 
tinctly bluer.  The  enclosed  is  somewhat  less  blue  due 
to  the  absorption  by  the  glass,  but  it  is  still  bluer  than  the 
candle.  The  flaming  arcs  vary  greatly,  but  none  of  them 
have  the  same  color  as  the  candle,  and  the  mercury  arc  is 
less  like  the  candle  than  any  of  the  others. 

Not  only  is  it  difficult  for  an  observer  to  compare  two 
unlike  colors  in  a  photometer,  but  different  observers  arrive 
at  results  differing  often  by  many  per  cent.  The  ideal 
method  would  be  one  giving  relative  values  for  practical 
purposes,  such  as  reading  a  paper  or  seeing  an  obstacle  in 
the  road,  but  unfortunately  we  have  no  way  of  making 
definite  comparisons  of  this  sort. 

126 


PHOTOMETRY  OF  THE   ELECTRIC  ARC 

A  second  difficulty  is  due  to  the  continuous  fluctuation 
of  the  arc.  An  arc  between  the  better  kinds  of  carbons 
can  be  kept  fairly  steady  by  constant  regulation,  although 
even  then  sudden  changes  are  apt  to  occur.  But  even  if 
satisfactory  measurements  are  made,  one  has  no  very 
definite  knowledge  of  the  candle  power  of  the  lamp  when 
run  under  commercial  conditions  where  the  regulation  of 
the  lamp  is  not  perfect.  Fortunately,  where  cored  carbons 
are  used  for  the  anode,  this  difficulty  is  not  as  great  as  it 
is  with  solid  carbons. 

A  third  difficulty  is  due  to  the  irregular  distribution  of 
the  light.  There  is  no  form  of  artificial  light  which  is 
equally  luminous  in  all  directions,  but  the  common  form 
of  the  arc  has  the  disadvantage  that  there  are  two  direc- 
tions in  which  the  mechanism  of  the  lamp  obstructs  the 
light.  Moreover  the  distribution  of  light  from  a  direct- 
current  arc  is  not  symmetrical  about  these  two  ends.  This 
can  well  be  seen  by  referring  to  Fig.  39  taken  from  the  data 
of  Fleming  and  Petavel.1  O  is  the  arc.  The  intensity  of 
light  in  any  direction  is  indicated  by  the  curved  line  and 
is  proportional  to  the  distance  of  this  line  from  the  arc  0. 

Again  the  center  of  the  arc  is  usually  at  one  side  of  the 
center  of  the  carbons  and  wanders  from  one  place  to  an- 
other. As  a  result  the  distribution  of  the  light  about  a 
vertical  axis  is  unsymmetrical  and  the  intensity  in  any 
direction  will  vary  from  time  to  time. 

Because  of  the  irregular  distribution  of  light  from  the 
arc,  it  means  nothing  to  say  that  an  arc  has  a  certain 
candle  power,  unless  some  definite  direction  is  also  given. 
An  arc  light  of  1000  candle  power  might  be  a  very  good 
light  or  a  poor  one,  depending  on  the  direction  in  which  the 

i  Phil.  Mag.,  (5),  41*  3555  1896. 


128 


THE   ELECTRIC  ARC 


light  was  measured.  Because  of  this  irregular  distribution 
the  average  intensity  over  a  part  or  the  whole  of  the  region 
illuminated  is  often  given.  If  the  average  intensity  in  all 
directions  is  given,  it  is  called  the  mean  spherical  candle 
power  (abbreviated  to  m.s.c.p.).  Since  the  part  of  the  light 
which  is  thrown  below  the  horizontal  plane  passing  through 


o°a 


1500 


the  light  is  all  that  is  useful  in  the  majority  of  cases,  meas- 
urements are  often  made  of  this  part  alone  and  the  aver- 
age of  this  is  called  the  mean  hemispherical  candle  power 
(m.h.s.c.p.). 

Some  of  the  measurements  given  in  the  following  pages  are 
taken  from  German  sources  and  are  given  in  hefner  units. 
One  hefner  unit  is  equivalent  to  0.88  English  candle. 

Distribution  of  Light.  —  With  the  common  form  of  the 
carbon  arc  the  greater  part  of  the  light  comes  from  the 


PHOTOMETRY  OF  THE  ELECTRIC  ARC      I2p 

crater  of  the  anode.  The  cathode  gives  a  small  amount, 
but  obstructs  more  than  it  gives  out,  while  the  gas  between 
the  carbons  absorbs  as  much  as  or  perhaps  more  than  it 
gives  out.  The  first  person  to  give  any  statement  con- 
cerning the  distribution  of  light  from  the  arc  which  could 
be  put  in  simple  form  was  Trotter.1  His  statement  was 
that  the  intensity  of  light  in  any  direction  was  approxi- 
mately proportional  to  the  component  of  the  area  of  the 
crater  which  was  perpendicular  to  and  visible  from  that 
direction.  Thus  above  a  in  Fig.  39  little  of  the  crater 
would  be  visible,  because  of  its  concave  shape,  and  what 
is  visible  would  have  but  a  small  component  perpendicular 
to  the  line  drawn  to  a.  As  seen  from  b  there  would  be 
a  large  component  perpendicular  to  the  line  drawn  to  b, 
while  at  c  it  would  be  largely  hid  by  the  cathode.  This 
statement  is,  of  course,  only  approximately  correct,  since 
some  light  comes  from  the  cathode  and  some  from  the 
vapor,  but  Trotter  showed  that  this  was  only  a  few  per  cent 
of  the  total  amount. 

The  value  of  an  arc  for  lighting  purposes  depends  to  a 
very  great  extent  on  the  distribution.  For  example,  the 
distribution  shown  in  Fig.  39  is  undesirable,  since  almost 
no  light  is  thrown  immediately  below  the  lamp  and 
very  little  in  a  horizontal  direction.  The  first  defect 
would  make  the  lamp  a  poor  one  for  indoor  lighting,  since 
there  would  be  a  considerable  dark  region  below  the  lamp. 
However,  such  lamps  are  not  often  used  for  indoor  work 
and  the  more  serious  defect  is  the  second  one.  Near  the 
lamp  there  will  be  light  enough  for  street  lighting  in  any 
case,  but  as  the  distance  increases  the  amount  of  light 
rapidly  diminishes,  both  because  the  distance  is  greater 

1  Lond.  Elec.,  28,  687;  and  29,  n;   1892. 


130  THE   ELECTRIC  ARC 

and  because  the  direction  is  nearly  horizontal.  For  ex- 
ample, if  a  lamp  giving  the  distribution  shown  in  Fig.  26 
were  hung  at  a  height  of  15  ft.,  the  light  striking  the  ground 
at  a  distance  of  150  ft.  would  make  an  angle  with  the 
horizontal  of  less  than  6  degrees,  and  the  candle  power  in 
this  direction  is  not  more  than  a  fourth  of  what  it  is  in  a 
direction  making  an  angle  of  50  degrees  with  the  horizontal. 

Effect  on  Candle  Power  Produced  by  Length  of  Arc, 
Current,  Etc.  —  From  the  statement  given  above  concern- 
ing the  distribution  of  light  it  follows  that  any  cause  affect- 
ing the  amount  of  the  crater  that  is  visible  from  any  given 
direction  affects  the  intensity  of  light  in  that  direction. 
Thus  the  shorter  the  arc  the  more  the  light  from  the  crater 
is  cut  off  by  the  cathode.  One  would  expect  from  this  that 
the  longer  the  arc  the  greater  would  be  the  candle  power. 
There  is  the  more  reason  to  expect  this,  since  there  is  more 
luminous  vapor  with  the  longer  arcs.  It  has  been  found, 
however,  that  the  candle  power  does  not  increase  indefi- 
nitely as  the  arc  is  lengthened,  but  reaches  a  maximum  and 
then  decreases  with  greater  length.  Thus  Ayr  ton  found  the 
maximum  candle  power  to  be  with  lengths  of  about  4  mm. 
Mrs.  Ayrton  plotted  curves  taken  from  the  data  of  Blondel.1 
These  are  reproduced  in  Fig.  40.  The  numbers  near  the 
curves  indicate  the  diameters  of  the  electrodes.  Those 
above  the  dash  indicate  the  diameter  of  the  anode  in  milli- 
meters; those  below,  the  diameter  of  the  cathode. 

From  this  it  would  appear  that  there  is  a  maximum 
candle  power  at  about  6  mm.  of  length.  Mrs.  Ayrton 
believed  the  decrease  with  greater  lengths  to  be  due  to 
the  absorbing  power  of  the  vapor  between  the  terminals. 

1  Mrs.  Ayrton's  "Electric  Arc,"  p.  333.  Eel.  Elec.,  10,  289,  496,  and 
539;  1897. 


PHOTOMETRY  OF  THE  ELECTRIC  ARC  I; 

Since  the  intensity  of  light  becomes  less  with  these  lengths 


15,000 


10/10  Soft 


3,000 


6  8  10 

LENGTH  IN  MM. 

FlG.   40. 


16  MM. 


and  the  power  consumed  becomes  greater,  the  ratio  be- 
tween the  two  becomes  rapidly  smaller  with  arcs  more 


than  a  few  millimeters  long. 

Fig.  40  illustrates  also  the 

difference  between  different 


5,000 


(£. 

HI 

|  4,000 

kinds  of  carbons  and  shows  y 
how  impossible  it  is  to  make  |  3.°°° 
any  definite  statement  con-  j 
cerning  the  candle  power  of  I  2i°00 
arc   lights,  or  to  give  any  J 
formula    which     will     hold 
with  different  carbons.     No 
two  kinds  of  carbons  vary 
in  the  same  way.     One  might 
almost  say  that  no  two  pairs 
of  carbons  of  the  same  make  show  the  same  results. 
Measurements  were  made  by  Ayrton  with  different  cur- 


0 
0 
0 


.<F 


10  20  30    35 

CURRENT  IN  AMPERES 


FIG.  41. 


132  THE   ELECTRIC  ARC 

rents  keeping  the  length  of  the  arc  constant,  and  by  Blondel l 
with  the  voltage  constant.  Fig.  41  reproduces  two  of  the 
curves  given  by  Ayrton.2  As  may  be  seen,  the  increase 
in  light  is  nearly  proportional  to  the  current  flowing.  Rey 
measured  the  candle  power  with  currents  up  to  250  amperes 
and  states  that  the  light  increases  more  rapidly  than  the 
current.3 

The  larger  the  carbons  the  less  the  candle  power,  due  to 
shading  of  the  light  from  the  crater  by  the  carbons.4  It  has 
also  been  found  that  there  is  a  loss  of  candle  power  when 
the  pressure  of  the  surrounding  gas  is  more  than  one  atmos- 
phere. This  is  due  to  the  presence  of  fumes  of  nitric  acid.5 

Intrinsic  Brightness  of  Crater.  —  For  many  purposes  the 
usefulness  of  a  light  depends  not  only  on  the  total  amount 
of  light,  but  also  on  the  amount  given  per  unit  area  of  the 
luminous  surface.  A  concentrated  light  is  often  blinding 
and  may  be  injurious  to  the  eye.  In  this  respect  all  forms 
of  the  arc  are  far  from  being  ideal  and  the  carbon  arc  is 
the  worst  of  all  lights.  Blondel  states  that  the  intrinsic 
brightness  of  the  crater  is  160  candles  per  sq.mm.  Petavel6 
found  a  value  of  147  candles  per  sq.mm.  for  a  current  density 
varying  from  0.06  to  0.26  ampere  per  sq.mm.  This  is 
something  like  200,000  times  the  brightness  of  a  candle 
flame. 

Flaming  Arcs.  —  The  previous  discussion  applies  to  the 
older  form  of  arc  where  by  far  the  greater  part  of  the  light 
comes  from  the  anode.  In  the  flaming  arcs  the  chief 

1  Eel.  Elec.,  10,  297;  1897. 

2  Mrs.  Ayrton's  "Electric  Arc,"  p.  366. 

3  Eel.  Elec.,  32,  in;  1902. 

4  Schreihage,  Centralbl.  f.  Elektrot.,  10,  604;  1888. 

5  Wilson,  Astrophys.  Journ.,  2,  212;  1895. 

6  Proc.  Roy.  Soc.,  65,  469;  1899. 


PHOTOMETRY  OF  THE   ELECTRIC  ARC  133 

source  of  light  is  the  long  luminous  vapor.     Because  of  the 
high  conductivity  of  this  vapor,  it  is  possible  to  have  very 
long    arcs    and   the  candle  power  is  ap- 
proximately proportional  to  the  length  of 
these  arcs. 

The  distribution  of  light  is  much  more 
symmetrical  than  with  the  more  common 
forms.  In  some  cases  this  is  a  disadvan- 
tage, as  when  the  light  is  needed  beneath 
the  lamp.  On  this  account  the  carbons 
are  sometimes  placed  nearly  parallel  and 
above  the  arc  as  shown  in  Fig.  42,  the 
arc  being  kept  below  by  means  of  a  magnet.  This  is  the 
same  plan  as  that  of  the  "Carbone"  lamp.1 

The  amount  of  light  depends  on  the  amount  of  substance 
added  to  the  carbon.  For  example,  the  candle  power  with 
different  percentages  of  calcium  fluoride  has  been  studied 
by  Wedding2  and  his  results  are  shown  in  Fig.  43.  The 
arc  with  which  he  worked  was  one  between  converging 
carbons  with  a  reflector  above.  In  each  case  there  was  a 
current  of  9  amperes  and  a  potential  difference  of  45  volts. 
The  amount  of  added  mineral  is  given  with  each  curve. 

The  efficiency  of  the  flaming  arc  varies,  of  course,  with 
different  makes  of  carbons  and  with  different  kinds  of 
lamps.  Sharp3  states  that  BlondePs  flaming  arc  requires 
between  0.16  and  0.18  watt  per  mean  lower  hemispherical 
candle  power,  which  is  less  than  one-fourth  of  that  of 
the  open  carbon  arc.  Marchant4  states  that  the  yellow 

1  Lond.  Elec.,  57,  51,  and  129;   1906. 

2  Elektrot.  ZS.,  23,  702;  1902. 

3  Trans.  Intern.  Elec.  Cong.,  St.  Louis,  2,  765;  1904. 

4  Elec.  World,  56,  216;   1910. 


134 


THE  ELECTRIC   ARC 


flaming  arc  requires  0.144  watt  per  mean  hemispherical 
candle  power,  and  the  white  flaming  arc  0.338  watt. 
Further  data  will  be  given  in  the  tables  at  the  end  of  this 
chapter,  but  for  an  adequate  knowledge  of  the  photometry 
of  these  lamps  reference  must  be  made  to  the  articles  con- 
stantly appearing  in  the  technical  journals.1 


60" 


Metal,  Including  Mercury,  Arcs.  —  As  far  as  I  have  been 
able  to  learn  no  measurements  have  been  made  on  the 
candle  power  of  arcs  between  metals  in  air.2  None  of  these 

1  See  also  Bloch,  Elektrot.  ZS.,  30,  703;   1909. 
Georges,  Elektrot.  ZS.,  30,  595;    1909. 
Heyck,  Elec.  World,  54,  863;    1909. 
Elektrot.  ZS.,  30,  1055;   1909. 

Monash,  Elektrot.  ZS.,  30,  341;   1909. 

2  This  does  not  include  arcs  having  one  terminal  an  oxide  of  metal  such 
as  the  magnetite  arc. 


PHOTOMETRY  OF  THE   ELECTRIC  ARC 


135 


have  ever  been  used  commercially,  and  there  is  little  object 
in  getting  their  candle  power  for  any  other  purpose. 

The  candle  power  of  the  mercury  arc  has  been  examined 
by  Kuch  and  Retschinsky.1  Their  measurements  were 
made  with  a  mercury  arc  in  a  quartz  tube  approximately 
27  cm.  long.  The  comparisons  were  made  with  standard 


1.0 


.8 


.2 


200 


400 


600     800 
WATTS 


1000   1200 


FIG.  44. 

incandescent  lamps  by  means  of  a  flicker  photometer. 
They  found  the  intensity  of  light  with  a  current  of  1.9 
amperes  and  voltage  of  27  volts  to  be  58  candles  (66  hefner 
units).  With  3.85  amperes  and  304  volts  the  candle  power 
was  6270.  In  Fig.  44  the  relation  is  shown  between  the 
watts  used  and  the  watts  per  hefner  unit. 

They  found  also  that  the  energy  of  the  ultra-violet  light 
per  watt  of  power  supplied  also  passed  through  a  maximum 
and  decreased  in  a  manner  similar  to  that  of  the  visible  rays. 

Alternating-current  Arcs.  —  The  chief  difference  between 
the  alternating-  and  direct-current  arcs  as  far  as  light- 

1  Ann.  d.  Phys.,  20,  568;  1906,  and  22,  852;  1907. 


136 


THE   ELECTRIC  ARC 


FIG.  45- 


giving  properties  are  concerned  is  that  with  the  latter  the 
greater  part  of  the  light  comes  from  only  one  of  the  ter- 
minals, namely  the  anode,  while  with  the 
former,  both  terminals  give  the  same 
amount  of  light,  the  anode  alternating  from 
one  to  the  other  terminal.  The  distribu- 
tion of  light  is,  accordingly,  that  shown  in 

Fig.  45- 

With  ordinary  frequencies  the  light  from 
the  alternating-current  arc  appears  to  the 
eye  to  be  continuous,  white  with  smaller 
frequencies  the  flickering  becomes  noticeable. 
Thus  Georges1  found  that  with  60  periods 
per  second  the  flickering  was  not  notice- 
able, while  with  40  periods  per  second  it  was  very  dis- 
agreeable. 

While  this  is  the  appearance  presented  to  the  eye, 
the  actual  amount  of  light  changes  very  appreciably  dur- 
ing an  alternation,  the  candle  power  corresponding  much 
more  closely  to  the  current  flowing  at  each  instant  than 
might  be  expected  when  one  remembers  that  the  crater 
must  be  heated  up  and  cooled  off  with  each  alternation. 
This  is  shown  by  curves  in  Fig.  46.  In  this  figure  the  curve 
marked  a  represents  the  potential  difference,  b  the  current, 
c  the  watts,  and  d  the  candle  power.  During  the  first  part 
of  the  alternation  the  photometer  was  illuminated  by  the 
light  of  the  anode.  During  the  second  part  this  carbon 
had  become  the  cathode  and  was  giving  much  less  light.2 
Duddell3  found  that  when  an  alternating  current  was 

1  Elektrot.  ZS.,  16,  548;  1895. 

2  See  also  Leonard,  Eel.  Elec.,  42,  241;   1905. 

3  Lond.,  Elec.,  46,  270;  1900. 


PHOTOMETRY  OF  THE  ELECTRIC  ARC 


137 


superimposed  on  a  direct  current,   changes  in  the  light 

could  be  observed  when  the  change  in  the  current  was  only 

3    per    cent   of    the 

total     current     and 

when     there      were 

4300  alternations  per 

second. 

The  alternating- 
current  arc  is  not 
so  efficient  as  the 
one  with  direct  cur- 
rent.1 A  compari- 
son of  the  two  for 
different  currents  is 

given  in  Fig.  47.  Matthews  gave  the  candle  power  per 
watt  for  the  direct-current  enclosed  arc  as  0.76,  for  the 
alternating-current  arc  without  reflector  as  0.53  and  with 
reflector  as  0.68. 

This  form  of  arc  is  influenced  by  length,  amount  of  cur- 
rent and  size  of  carbons  much  the  same  as  the  direct-current 
arc  is.  Thus  the  watts  per  candle  power  become  greater 
as  the  arc  becomes  longer.  This  is  shown  in  Fig.  48,  taken 
from  the  work  of  Fleming  and  Petavel.  The  candle  power 
is  less  the  larger  the  diameter  of  the  carbon  used  and  in- 
creases approximately  as  the  current.2 

The  candle  power  per  watt  has  been  found  to  depend 
both  on  the  wave  form  of  the  current  and  on  the  number 
of  alternations  per  second.  Rossler  and  Wedding3  found 

1  Fleming  and  Petavel,  Phil.  Mag.,  (5),  41,  359;   1896. 
Dyke,  Phil.  Mag.,  (6),  10,  216;   1905. 

Elektrot.  ZS.,  23,  615;   1902. 

2  Blondel  and  Jigouzo,  Elec.  World,  29,  232;  1897. 

3  Elektrot.  ZS.,  15,  315;  1894. 


138 


THE   ELECTRIC  ARC 


£00  | 


300  400  500 

WATTS  EXPENDED  IN  ARC 


FIG.  47. 


600 


PHOTOMETRY  OF  THE   ELECTRIC  ARC 


139 


that  with  a  pointed  form  there  was  0.710  hefner  unit  per 
watt  and  that  for  a  flat  curve  there  were  1.024  hefner 
units.  They  also  found  that  the  candle  power  decreased 
as  the  number  of  alternations  increased. 

Comparison  of  Different  Kinds  of  Arcs.  —  A  comparison 
of  candle  power  of  different  arc  lamps  has  been  made  by 
Blondel1  and  his  results  are  given  in  the  following  table. 


Watts. 

fl 

fc. 

la 

i  ^  C 

Type  of  lamp. 

j 

§i 

O.<" 

i| 

o  O  Q 

8  §.2 
£•'•§,8 

H 

1 

Is 

•a 

v>  S 

3^2 

§ 

1 

*o 

O 

w  rf 

O  9  H 

o 

> 

13 

H 

g« 

£>  ° 

W  W+J 

Ordinary  pure  carbon  lamp1  
Ordinary  pure  carbon  lamp1  
Flaming  arc,  vertical  carbon1  

9 
9 
9 

40 
35 
40 

360 
315 
360 

495 
330 
495 

700 
540 
910 

0.514 
0.583 
0.396 

16-17 
16-17 
27.5 

Flaming  arc,  converging  carbon1  
Enclosed  arcs  2  

9 
6.8 

45 
70 

405 
476 

495 
768 

20OO 
329 

0.202 

1-45 

34-42.5 
1.5-2 

Magnetite  arcs3  

3-5 

91 

320 

385 

400 

0.80 

1-2 

Bremer  lamp* 

9 

48 

432 

495 

4814 

0.088 

35-45 

Blondel  lamp  9  amperes  5  
Mercury  arc6. 

9-1 
3-5 
3-5 

43 
80 
48.3 

391 
280 
169 

500 
385 
385 

4800 
770 
700 

0.081 
0.362 

0.242 

1-2 

Iron-titanium  arc7  

"Lambe  Carbonne"8  

10 

90 

900 

IIOO 

I07O 

0.84 

I9-2O 

Alternating-current  Lamps. 


Ordinary  pure  carbon1. 

9 

30 

270 

33O 

35o 

o  772 

Ordinary  cored  carbon  9  

15 

35 

480 

555 

470 

1.  02 

15-16 

Flaming  arc,  vertical  carbon  

9 

Q 

30 

45 

270 

405 

330 

495 

700 

2OOO 

0.386 

O   2O2 

30 

35-45 

Enclosed  arcs2  
Blondel  lamp9                                

6.6 
10 

70 
35 

462 
255 

726 
37o 

314 
1890 

1-47 
o  135 

1-2 

I5-l6 

8 

33 

225 

372 

o  225 

I5-l6 

Zeidler,  Elektrotechnishe  Verein  von  Berlin,  Dec.  23,  1902. 

Matthews,  second  report,  p.  30,  and  third  report,  p.  17,  N.  E.  L.  A.  A. 

M.  W.  Holmes,  Elec.  World,  43,  1053;  1904. 

Czudnochowski,  Vertrag  der  Deutschen  Phys.  Gesellschaft,  1903,  No.  7. 

Essais  des  Laboratoire  de  la  Soc.  Auer  de  Paris. 

Westinghouse  circular. 

Ladoff  Eel.  Elec. 

Monash,  Elektrische  Beleutung,  p.  179. 

Essais  des  Laboratoire  central  d'Electricite  de  Paris. 


1  Trans.  Intern.  Elec.  Cong.,  St.  Louis,  2,  755;  1904.     Eel.  Elec.,  52, 
68;  1907. 


140  THE   ELECTRIC  ARC 

A  more  recent  comparison  of  direct-current  arc  lamps 
has  been  given  by  Ryan1  in  which  the  following  lamps 
were  compared. 

(1)  The  carbon  open  arc,  9.6  amperes,  50  volts,  consum- 
ing in  practice  from  450  to  500  watts,  commercially  rated 
at  480  watts,  equipped  with  clear  globe  and  no  reflector. 
Electrode  life  of  from  16  to  18  hours.     This  lamp  is  nor- 
mally designated  as  2000  c.p.,  which,  however,  is  regarded 
as  merely  a  trade  name. 

(2)  Enclosed  carbon  arc,  requiring  6.6  amperes  and  from 
70  to  75  volts,  consuming  in  practice  from  450  to  500  watts, 
commercially  rated  at  480  watts,  equipped  with  light  opal 
inner,  clear  outer  globe  and  street  reflector.     Electrode  life 
of  from  100  to  150  hours. 

(3)  Magnetite  arc,  requiring  4  amperes  and  from  75  to  80 
volts,  consuming  in  practice  from  300  to  320  watts,  com- 
mercially rated  at  310  watts,  equipped  with  clear  outer 
globe,  internal  concentric  diffuser  and  magnetite  electrode. 
Electrode  life  of  from  150  to  200  hours. 

(4)  Magnetite  arc,  requiring  6.6  amperes,  75  to  80  volts, 
consuming  in  practice  from  495  to  530  watts,  commercially 
rated  at   510  watts,  equipped  with  clear  globe,  internal 
concentric  diffuser  and  magnetite  electrode.     Electrode  life 
of  from  75  to  125  hours  (large  unit). 

(5)  Boston  flaming  arc,  requiring  from  6.6  amperes  and 
from  75  to  80  volts,  consuming  in  practice  from  495  to  530 
watts,  commercially  rated  at   510  watts,   equipped  with 
26-in.    concentric    diffuser    and    light    opal    outer    globe. 
Electrode  life  of  from  20  to  25  hours. 

The  following  are  the  data  which  he  gives  concerning 
these. 

1  Paper  presented  before  the  N.  E.  L.  A.,  at  St.  Louis,  1910. 


PHOTOMETRY  OF  THE   ELECTRIC  ARC 


141 


Watts 

Watts 

rp     ,  i 

Down- 

Lamps. 

Amps. 

Volts. 

Watts. 

H.S.C.P. 

H.S.C.P. 

S.C.P. 

per 
S.C.P. 

iotal 
lumens. 

ward 
lumens. 

Open  Arc  

9-6 

50 

480 

813 

0.59 

540 

0.89 

6,800 

5,100 

Enclosed  Arc  .  . 

6.6 

70-75 

480 

505 

0.95 

3io 

1.55 

3,900 

3,i8o 

Luminous  Arc  . 

4 

75-8o 

310 

523 

0.59 

276 

1.  12 

3,5oo 

3,3oo 

Luminous  Arc  . 

6.6 

75-80 

5io 

1328 

0.38 

7i8 

0.71 

9,000 

8,300 

Flame  Arc  

6.6 

75-80 

5io 

2964 

0.17 

1821 

0.28 

23,000 

18,600 

The  curves  showing  the  distribution  of  light  for  these 
arcs  are  given  in  Fig.  49.     While  the  total  quantity  of  light 


FIG.  49. 

emitted  by  the  open  carbon  arc  is  greater  than  that  for 
either  the  closed  arc  or  for  the  first  form  of  the  magnetite 
arc,  it  will  be  seen  from  the  curves  that  the  amount  sent 
in  a  horizontal  direction  is  less  for  this  arc  than  for  any  of 


142  THE   ELECTRIC   ARC 

the  others,  and  the  value  of  a  lamp  for  street  lighting  de- 
pends very  largely  on  the  amount  sent  in  this  direction. 
This  is  partly  responsible  for  the  fact  that  the  open  arc  has 
been  superseded  to  a  very  great  extent  by  other  forms. 

The  figures  for  the  flaming  arc  show  a  very  low  value  of 
the  watts  per  candle  power  and  also  a  very  desirable  dis- 
tribution of  the  light.  In  the  first  of  these  respects  it  excels 
any  other  form  of  light. 

In  1908  a  report  was  submitted  to  the  German  Govern- 
ment1 in  which  they  gave  the  light  intensity  in  hefner  units 
per  kilowatt  for  different  sources  of  light  as  follows: 

Common  form  incandescent  filament  lamps 300 

Improved  incandescent  filament  lamps 500 

Nernst  and  tantulum  incandescent  lamps. ; 500 

Osram  and  tungsten from  700-1000 

Alternating-current  arc  between  cored  carbons 800 

Direct-current  arc  between  cored  carbons 1000 

Direct-current  flaming  arc 2000 

Mercury  vapor  arc 1600 

Mercury  vapor  arc  in  quartz  tube 3000 

Spectrum  of  the  Arc.  —  The  spectrum  of  the  terminals 
of  the  arc  is,  of  course,  the  continuous  spectrum  of  an  in- 
candescent solid  and  does  not  differ  from  that  of  other 
incandescent  solids. 

Unfortunately,  no  such  simple  statement  can  be  made 
concerning  the  spectrum  of  the  gaseous  part.  Instead  of 
some  simple  spectrum  of  carbon  monoxide,  for  example, 
with  an  occasional  line  due  to  some  impurity  in  the  carbon, 
there  is  one  so  complicated  that  it  is  not  possible  to  deter- 
mine the  cause  of  all  the  lines.  There  are  not  only  lines  due 
to  all  the  impurities  which  would  be  expected,  but  many 
due  to  impurities  which  would  not  be  expected. 

1  La  Revue  Elec.,  Jan.  15,  1909. 


PHOTOMETRY  OF  THE  ELECTRIC  ARC 


FIG.  50. 


In  addition  the  spectra  of  different  parts  of  the  arc  show 
decided  differences.  The  arc  has  indeed  been  divided  into 
two  or  three  different  regions  by  those  who 
have  examined  its  spectrum.  This  is  more  or 
less  arbitrary  but  will  help  us  to  gain  some 
idea  of  the  colors  in  different  parts.  For  ex- 
ample, Foley1  divided  the  carbon  arc  into 
three  parts,  as  shown  in  Fig.  50.  The  first 
region  is  violet,  the  second  is  blue  and  the 
third  yellow.  At  times  the  first  region  ex- 
tends entirely  across  from  the  anode  to  the 
cathode.  At  other  times  it  extends  only 
part  way  as  shown  in  the  diagram. 

The  spectra  of  all  parts  show  a  great  many  lines. 
Many  of  these  belong  to  the  carbon  spectrum,  but  even 
when  the  purest  carbon  is  used,  there  are  also  many  lines 
which  can  be  identified  as  lines  of  various  metals.  There 
are  also  many  lines  about  which  there  is  still  more  or  less 
dispute.  It  can  not  be  definitely  stated  whether  these  are 
carbon  lines  or  metallic  lines  which  do  not  ordinarily  show 
in  the  spectrum,  but  are  brought  out  by  the  peculiar  con- 
ditions of  the  arc. 

The  number  of  lines  in  the  spectrum  of  the  first  region 
is  much  greater  than  in  those  of  the  other  two.  This  is 
due  chiefly  to  the  fading  out  of  carbon  bands  in  the  second 
and  third  regions,  but  the  lines  of  metals  also  show  the 
same  tendency.  Foley  found  the  third  part  to  be  composed 
largely  of  vapor  of  calcium  and  iron. 

Miss  Baldwin2  found  that  the  carbon  bands  showed  more 
clearly  at  the  positive  pole  and  the  metallic  lines  at  the 

1  Phys.  Rev.,  5,  129;  1897. 

2  Phys.  Rev.,  3,  370;  1895. 


144  THE  ELECTRIC  ARC 

cathode.  Hull1  makes  a  similar  statement  for  currents  of 
only  a  few  amperes,  but  states  that  with  the  hissing  arc 
the  metallic  spectra  appeared  at  both  poles. 

When  metals  were  introduced  into  the  arc,  Miss  Baldwin 
found  that  the  more  positive  ones,  such  as  potassium, 
sodium,  lithium,  barium,  strontium  and  calcium  appeared 
at  the  cathode  more  brightly  than  those  less  electropositive, 
such  as  cadmium,  zinc,  copper  and  silver. 

One  of  the  most  important  observations  on  the  spectrum 
of  the  arc,  provided  it  is  correct,  was  made  by  Lenard.2 
He  states  that  the  arc  consists  of  different  layers  and  that 
different  series  of  lines  of  the  spectrum  of  a  given  element 
appear  in  these  different  layers.  Thus,  if  sodium  is  intro- 
duced into  the  arc,  only  the  principal  series  of  the  spectrum 
appears  in  the  outside  layer.  The  first  subordinate  series 
of  lines  appears  in  an  inner  layer  of  vapor  and  the  second 
subordinate  series  in  a  layer  within  this.  An  absorbing 
medium  which  cuts  out  all  of  the  lines  except  the  principal 
series,  shows  all  of  the  vapor  of  the  arc.  A  medium  leaving 
only  the  first  subordinate  series  will  show  an  inner  cone, 
but  not  the  whole  luminous  vapor. 

Lenard's  explanation  is  that  the  atoms  of  an  element  are 
acted  on  differently  in  different  parts  of  the  arc  and  that 
each  series  is  produced  by  one  particular  method  of  ex- 
citation. The  experiment  itself  has  been  verified  by 
Puccianti.3  On  the  other  hand  Kayser4  does  not  agree 
with  Lenard  but  thinks  that  what  he  observed  was  due  to 
varying  intensity  of  the  different  lines  in  different  parts  of 
the  arc. 

1  Astro-phys.  Journ.,  28,  59;  1908. 

2  Ann.  d.  Phys.,  n,  636;  1903. 

8  N.  Cimento,  (5),  13,  268;   1907.    Phys.  ZS.,  8,  463;   1907.   , 
4  Sz.  wiss.  Phot.,  6,  68;  1908. 


PHOTOMETRY  OF  THE   ELECTRIC  ARC  145 

The  matter  is  one  of  much  importance  from  a  theoretical 
point  of  view,  as  almost  nothing  is  known  concerning  the 
reason  why  very  different  spectra  are  given  by  the  same 
element  under  different  circumstances.  A  knowledge  of 
the  cause  for  this  difference  would  undoubtedly  throw  much 
light  on  the  construction  of  the  atom  and  its  behavior  when 
disturbed  by  electrical  discharge.  Even  if  the  phenomena 
are  not  as  simple  as  was  supposed  by  Lenard,  there  still  is 
no  question  but  that  the  spectra  of  elements  differ  in 
different  parts  of  the  arc  and  a  further  study  of  these 
variations  may  throw  light  on  this  question. 

An  examination  of  the  spectra  of  the  arc  under  different 
pressures  has  been  made  by  Humphreys.1  He  found  that 
as  the  pressure  increased  the  width  of  the  lines  increased, 
some,  however,  more  than  others.  The  metallic  lines  were 
somewhat  displaced;  the  carbon  lines  were  not. 

The  statement  has  been  made  by  Steinmetz2  that  in 
general  the  spectrum  of  the  arc  is  that  of  the  cathode 
material.  This,  however,  would  appear  to  be  true  only 
when  the  anode  is  not  heated  to  a  temperature  sufficiently 
high  to  vaporize  it.  With  a  carbon  anode  in  air,  or  with 
the  majority  of  metals  in  air  this  does  not  appear  to  be  the 
case.  Cady  and  Arnold,  for  example,  found  that  with 
ordinary  currents  the  spectrum  of  the  anode  was  very 
apparent.3 

1  Astro-phys.  Journ.,  26,  18  and  36;  1907. 

2  Trans.  Intern.  Elec.  Cong.,  St.  Louis,  2,  711;  1904. 

3  Further  work  has  been  done  by  the  following: 

Snow,  Phys.  Rev.,  I,  108;   1893. 

Duffield,  Astro-phys.  Journ.,  26,  375;   1900. 

Hallwachs,  Ann.  d.  Phys.,  13,  38;    1904. 

Crew,  Astro-phys.  Journ.,  20,  274;   1904. 

Crew  and  Spence,  Astro-phys.  Journ.,  22,  199;   1905. 


CHAPTER  VIII. 


USE  OF  ARC  IN  WIRELESS  TELEPHONY. 

Whispering  Arc.  —  The  electric  arc  has  been  used  in 
two  different  systems  for  wireless  telephony.  The  first  of 
these  had  its  origin  in  a  discovery  made  by  Simon  in  1898. 1 
While  working  with  an  arc,  he  observed  that  it  gave  a 
chattering  noise  whenever  an  induction  coil  in  a  neigh- 
boring room  was  operated.  He  found,  on  examination,  that 
for  several  feet  the  feed  wires  for  the  induction  coil  were 

parallel  to  those  running  to  the 
arc.  With  each  variation  of  the 
current  in  the  induction  coil 
there  was  an  induced  current  in 
the  arc  circuit,  and  with  each 
fluctuation  of  the  current  in  the 
arc  circuit  there  was  an  expan- 
sion and  contraction  of  the 
vapors  of  the  arc  which  sent  out 
sound  waves. 

This  suggested  to  him  the  idea 
that  instead  of  the  induction  coil 
the  transmitter  of  a  telephone 
could  be  used  and  the  arc  be 
made  to  reproduce  the  sound  of 


— 'nnnnnnp — -*" 


nnnnnnnn 

p     1 

T 


FIG.  51. 


the  words  spoken  into  the  transmitter,  and  on  trying  the 

experiment  this  was  found  to  occur.     In  order  to  increase 

1  Wied.  Ann.,  64,  233;  1898. 

146 


USE  OF  ARC  IN  WIRELESS  TELEPHONY  147 


the  effect  the  parallel  wires  were  replaced  by  an  induction 
coil  as  shown  in  Fig.  51.  M  is  the  microphone  which  is 
placed  in  series  with  a  cell  and  with  P,  the  primary  of  the 
induction  coil.  The  secondary  of  this  coil  is  placed  in 
series  with  the  arc. 

Braun,  in  the  same  year,1  stated  that  the  larger  the  cur- 
rent flowing  through  the  arc,  the  greater  the  change  in  the 
amount  of  energy  of  the  arc,  when  a  small  E.M.F.  is  in- 


duced in  the  arc  circuit.  This  would  be  true  if  the  current 
in  the  arc  obeyed  Ohm's  law,  but  since  it  does  not,  we  can 
not  find  from  theory  the  best  conditions  for  large  changes 
in  the  energy  of  the  arc. 

Several  methods  have  been  used  in  connecting  the  micro- 
phone in  the  circuit.2  A  very  common  one  is  that  shown 
in  Fig.  52,  where  the  microphone  M  is  in  shunt  with  an 
inductive  resistance  /,  so  that  each  change  in  the  resistance 

1  Wied.  Ann.,  65,  358;  1898. 

2  Ruhmer,  Elektrot.  ZS.,  22,  197;  1901,  and  23,  859;  1902. 
Simon,  Elektrot,  ZS.,  22,  510;  1901. 

Duddell,  Lond.  Elec.,  46,  269;  1900. 


148  THE  ELECTRIC  ARC 

of  the  microphone  causes  a  change  in  the  current  through 
the  arc. 

In  making  a  receiver  for  this  kind  of  wireless  telephone 
use  was  made  of  two  facts;  first,  that  with  each  change  of 
the  current  through  the  arc  there  is  a  change  in  the  intensity 
of  the  light  of  the  arc;  and  second,  that  the  electrical  re- 
sistance of  selenium  changes  whenever  the  intensity  of  the 
light  falling  on  it  changes,  so  that  selenium  may  be  used 
to  detect  changes  in  the  current  through  the  arc.  This 
is  done  by  making  the  selenium  one  of  the  arms  of  a  Wheat- 
stone  bridge  and  putting  a  telephone  receiver  in  the  place 
of  the  galvanometer.  By  using  an  unusually  sensitive 
piece  of  selenium  Ruhmer  was  able  by  such  an  arrangement 
to  send  messages  seven  kilometers. 

However,  this  method  has  not  been  found  to  be  a  com- 
mercial success.  In  the  first  place  it  can  be  used  only 
when  the  light  of  the  arc  shines  on  the  receiving  apparatus. 
A  fog,  for  example,  would  destroy  its  usefulness.  Again 
there  can  be  no  building  or  elevation  obstructing  the  view 
between  the  transmitter  and  the  receiving  apparatus. 
Moreover  the  system  can  not  be  used  in  the  daytime,  for 
changes  in  the  intensity  of  the  light  due  to  any  change  in 
the  light  of  the  arc  are  very  small  as  compared  with  ordinary 
daylight,  and  finally  under  the  most  favorable  conditions 
the  sound  received  is  but  a  poor  imitation  of  that  spoken. 

Whistling  Arc.  —  The  second  device  for  wireless  teleph- 
ony has  been  somewhat  more  successful.  It  depends  on 
a  discovery  which  appears  to  have  been  first  made  by 
E.  Thomson  in  1892 1  and  later  in  a  slightly  modified  form 
by  Duddell.2  The  principle  of  the  discovery  was  the  same 

1  U.  S.  Patent  No.  500,630. 

2  Lond.  Elec.,  46,  310;  1900.    Inst.  Elec,  Eng.,  30,  232;  1900. 


USE   OF  ARC  IN  WIRELESS   TELEPHONY  149 

in  both  cases,  i.e.,  that  when  a  condenser  with  self-induction 
in  series  with  it  is  shunted  about  an  arc,  oscillations  may 
be  produced  in  the  arc.  The  connections  are  shown  in 
Fig.  53  where  A  is  the  arc,  C  the  condenser,  72  the  induc- 
tance in  series  with  condenser,  and  K  a  key  for  opening  or 
closing  this  circuit.  In  general  for  the  production  of  the 
oscillations  it  is  necessary  to  have  an  arc  of  high  resist- 
ance and  a  shunt  circuit  with  low  resistance.  For  example, 


FIG.  53. 

solid  carbons  must  be  used  instead  of  cored  carbons.  The 
nearer  the  arc  is  to  extinction  without  being  extinguished 
the  more  apt  it  is  to  give  the  oscillations.  With  the  appa- 
ratus as  shown  by  Duddell  it  was  necessary  to  have  less 
than  2  ohms  in  the  shunt  circuit  with  about  5  millihenrys 
inductance  and  a  capacity  of  from  i  to  5  microfarads. 

This  is  due  to  the  fact  that  when  the  current  through  the 
arc  increases,  the  potential  difference  needed  to  produce 
it  decreases.  Thus,  if  the  key  at  K,  Fig.  53,  is  closed  while 
the  current  is  flowing  through  the  arc,  the  current  will  rush 
into  the  condenser.  If  there  is  also  inductance  at  /i,  the 
current  flowing  from  the  battery  will  not  have  time  to 
change  more  than  a  slight  amount  during  the  period  that 
the  condenser  is  being  charged.  Under  these  circum- 
stances the  current  which  rushes  into  C  will  be  taken 


THE   ELECTRIC  ARC 


from  that  which  had   previously   been   flowing   through 
the   arc. 

A  larger  potential  difference  will  be  needed  to  force  this 
smaller  current  through  the  arc,  as  may  be  seen  from 
Fig.  54  which  gives  diagrammatically  the  relation  between 


C    CURRENT 


FIG.  54. 


the  potential  difference  and  the  current  of  the  arc.  Thus 
let  Ob  represent  the  sum  of  the  currents  flowing  to  the  arc 
and  the  condenser.  Let  ab  represent  the  current  flowing 
into  the  condenser  at  some  given  moment.  Oa  will  then 
be  the  current  flowing  through  the  arc.  W  is  the  potential 
difference  at  the  terminals  of  the  arc  when  no  current  is 
flowing  to  the  condenser,  and  the  larger  quantity,  aa',  is 
the  potential  difference  when  part  of  this  current  is  flow- 
ing to  the  condenser. 

There  will,  however,  be  a  limit  to  the  increase  in  the 
voltage  which  can  be  supplied  to  the  arc  and  when  this  is 


USE  OF  ARC  IN  WIRELESS  TELEPHONY  151 

reached,  the  condenser  will  cease  taking  current  from  the 
arc,  the  arc  will  require  less  voltage,  and  the  condenser  will 
begin  to  discharge  through  it.  This  added  current  will  cause 
the  voltage  of  the  arc  to  drop  still  more  until  it  reaches 
the  value  shown  by  the  line  cc' .  Eventually  a  limit  will 
be  reached  in  this  direction  also.  As  the  current  from  the 
condenser  ceases  to  flow  through  the  arc,  its  voltage  begins 
again  to  increase  and  the  process  will  be  repeated. 

Energy  is  used  in  the  condenser  circuit  both  to  produce 
the  heat  due  to  the  resistance  of  the  circuit  and  to  radiate 
electrical  waves.  This  energy  is  given  to  the  condenser 
circuit,  because  the  potential  difference  is  higher  when  the 
current  is  flowing  into  the  condenser  than  it  is  when  it  is 
flowing  out,  so  that  more  energy  is  delivered  to  the  circuit 
than  is  received  from  it.  The  steeper  the  characteristic 
curve  of  the  arc  the  more  the  energy  that  will  be  delivered 
to  the  condenser  circuit.1  It  has  also  been  shown  by 
Simon2  that  the  greater  the  hysteresis  of  the  " dynamical" 
characteristic  curves,  the  greater  will  be  the  amount  of 
energy  delivered  to  the  condenser. 

In  general,  arcs  having  steep  characteristics  are  those 
having  terminals  which  cool  off  quickly,  or  those  whose 
resistance  is  in  some  way  artificially  increased.  Thus  it 
has  been  found  that  an  arc  between  copper  terminals  can 
be  used  for  producing  oscillations  to  better  advantage 
than  one  between  carbons  and  that  deflecting  the  arc  with 
a  magnet  is  advantageous.3  Increasing  the  pressure  of  the 

1  Granqvist,  Mitt.  d.  konigl.  Ges.  D.  Wiss.  zu  Upsala,  (4),  I,  62;   1906. 
Beib.,  31,  840;   1906. 

2  Phys.  ZS.,  4,  737;  1903,  6,  297;  1905,  and  7,  433;  1906. 
Elektrot.  ZS.,  26,  818  and  839;   1905,  and  28,  295;   1907. 
Jahrbuch  der  drahtlesen  Telegraph,  und  Teleph.,  I,  16;   1907. 

8  Poulsen,  Elektrot.  ZS.,  27,  1040;  1906. 


152  THE  ELECTRIC  ARC 

surrounding  gas  is  helpful,  and  surrounding  the  arc  with 
steam,  coal  gas  or  hydrogen  gives  better  results.1 

The  time  that  is  taken  for  charging  and  discharging  the 
condenser  depends  on  the  capacity  and  inductance  of  the 
condenser  circuit.  The  period  of  the  swing  would  equal 
2  irV~LC,  if  the  resistance  of  the  arc  were  constant,  and  it 
was  indeed  suggested  by  Janet2  that  use  could  be  made  of 
this  fact  to  determine  the  coefficient  of  inductance  of  any 
circuit  placed  in  series  with  the  condenser.  However,  the 
very  existence  of  the  phenomenon  depends  on  the  fact 
that  the  resistance  of  the  arc  is  not  constant  and  it  has  been 
shown  that  the  period  of  oscillation  depends  not  only  on 
the  capacity  and  inductance,  but  also  on  several  other  of 
the  conditions  under  which  the  arc  is  working,  so  that  this 
method  can  not  be  used  in  determining  inductance.3 

The  charging  and  discharging  of  the  condenser  produce 
electric  waves  and  it  is  possible  to  make  use  of  these  in 
wireless  telephony,  but  in  order  to  send  a  sufficient  amount 
of  energy  out  into  space,  it  is  necessary  to  have  high  fre- 
quency. Many  arcs  which  show  steep  characteristic  curves 
for  slow  changes  do  not  have  steep  curves  when  the  changes 
are  very  rapid,  as  has  been  shown  by  Duddell  for  carbon 
arcs.  If,  therefore,  oscillations  are  to  be  produced,  it  is 

1  A  very  complete  review  of  this  subject  showing  oscillographs  of  several 
different  arcs  has  been  given  by  Blondel.     (Eel.  Elec.,  44,  41  and  81;  1905.) 

2  C.  R.,  134,  462  and  821;  1902. 

3  Ascoli  and  Manzetti,  Rend.  Ace.  Line.,  (5),  n,  2  sem.  n;  1902. 
Corbino,  Sc.  Ab.,  7,  537;  1903. 

Duddell,  Lond.  Elec.,  I,  902;  1903. 

Maisel,  Phys.  ZS.,  4,  532;  1903. 

Salomonson,  Sc.  Ab.,  6,  167;  1903;  Eel.  Elec.,  34,  202;  1903. 

Granqvist,  Boltzmann  Festschrift,  799;  1904. 

Heinke,  Ver.  d.  Ver.  z.  Beford.  d.  Gewerbfleisses,  83,  403;  1904. 

Nasmith,  Phys.  Rev.,  27,  117;  1908,  and  32,  69;  1911. 


USE  OF  ARC  IN  WIRELESS   TELEPHONY 

necessary  to  use  arcs  which  not  only  have  steep  character- 
istic curves,  but  also  have  such  curves  for  rapid  oscillations. 
Among  the  different  forms  of  arc  which  have  been  used 
successfully  is  that  with  graphite  terminals.  Austin1  has, 
given  the  following  data  concerning  such  an  arc. 

Electrodes graphite,  ends  flat.. 

Diameter 12  mm. 

Resistance  in  series  with  arc ;  .  about  50  ohms. 

Arc  current 4  amp. 

Voltage  across  arc 26  volts. 

Voltage  open  circuit 242  volts. 

Arc  length about  0.3  mm. 

Inductance  in  shunt  circuit 0.009  millihenry. 

Capacity 0.4  micro-farad. 

Alternating  current  in  shunt 4  amp. 

He  found  still  better  results  with  the  arc  in  a  stream  of 
hydrogen  or  steam.  But  the  best  results  which  he  ob- 
tained were  with  the  arc  between  silver  terminals  in  air 
under  a  pressure  of  about  7  atmospheres  and  with  an  E.M.F. 
of  4500  volts.  The  arc  then  takes  on  all  the  characteristics 
of  a  very  rapid  spark  discharge  and  it  is  possible  to  develop 
a  large  amount  of  power  in  the  shunt  circuit. 

Applications  of  the  "  Whistling  "  Arc  to  Wireless  Te- 
lephony. —  The  application  of  the  whistling  arc  to  wireless 
telephony  is  a  subject  belonging  to  works  on  that  subject 
and  can  not  be  adequately  treated  here.  However,  two 
diagrams  are  given  which  show  how  the  arc  is  connected 
to  the  other  parts  of  the  transmitting  apparatus,  so  as  to 
send  electric  waves  out  into  the  ether.  In  order  to  do  this 
two  additions  must  be  made  to  the  device  shown  in  Fig.  52. 
First  it  must  be  changed  so  that  modifications  may  be  made 
in  the  electric  oscillations  which  shall  correspond  to  the 

1  Bull.  Bureau  Standards,  3,  325;  1907. 


154 


THE   ELECTRIC  ARC 


vibrations  of  the  voice.     One  of  the  simplest  arrangements 
for  this  purpose  is  shown  in  Fig.  55.     A  is  an  arc  producing 


X    A 


rVWVVVW\A/V-i 


o 

«• — > 

M 


FIG.  55. 


oscillations  in  the  circuit  ab.  If  is  a  microphone  producing 
disturbances  in  the  secondary  circuit.  P  is  the  primary 
•of  an  induction  coil  which  is  in  series  with  M.  S  is  the 
secondary  circuit  of  the  coil  and  is  in  series  with  the  arc. 

The  disturbances  in  P  induce 
currents  in  S.  These  currents 
modify  the  conditions  in  the  arc 
and  in  ab. 

The  oscillations  produced  by 
5  are  very  much  slower  than 
those  produced  by  the  arc,  so  that 
there  will  be  some  groups  of  waves 
sent  out  from  ab  which  are  some- 
what more  intense  than  other 
groups.  The  variations  in  these 
groups  will  correspond  to  the 


FIG.  56. 


vibrations  produced  in  the  microphone  M. 
A  second  manner  of  connecting  the  microphone  is  shown 


USE  OF  ARC  IN  WIRELESS  TELEPHONY      155 

in  Fig.  56,  where  the  microphone  is  placed  in  shunt  with 
the  inductance.  Changes  in  the  resistance  of  the  micro- 
phone will  again  produce  changes  in  the  intensity  of  the 
oscillations  about  the  arc. 

A  further  addition  must  be  made  to  the  apparatus  in 
order  that  the  oscillations  produced  by  the  arc  may  be 
radiated  into  space  and  to  do  this  effectively  it  is  necessary 
to  have  a  higher  E.M.F.  than  that  which  would  be  given 
by  the  device  already  described.  For  this  purpose  a  step- 
up  transformer  is  introduced  into  the  circuit  in  shunt  with 
the  arc  as  shown  in  Fig.  56,  where  P  is  the  primary  of 
the  transformer  and  S  is  the  secondary.  One  end  of  the 
secondary  is  connected  to  the  earth  and  the  other  to  an 
aerial  wire.1 

1  Partial  list  of  articles  published  on  the  second  method  of  wireless  teleph- 
ony which  I  have  not  otherwise  mentioned: 
Nussbaumer,  Phys.  ZS.,  5,  796;  1904. 
Ruhmer,  Elektrot.  ZS.,  27,  1060;   1906. 
Rozanski,  Beib.,  31,  845;   1907. 
Brown,  Lond.  Elec.,  58,  201;  1907. 
Vreeland,  Lond.  Elec.,  58,  685;  1907. 
Blondel,  Lond.  Elec.,  60,  216;   1907. 
Fessenden,  Lond.  Elec.,  59,  987;   1907. 
Mosler,  Elektrot.  ZS.,  28,  142;   1907. 
Fleming,  Lond.  Elec.,  59,  914;   1907. 
Sahulka,  Elektrot.  ZS.,  28,  1063;   1907. 
Traubenburg,  Elektrot.  ZS.,  28,  559;  1907. 
Eisenstein,  Elektrot.  ZS.,  28,  830;   1907. 
Schapira  and  Loewe,  Lond.  Elec.,  Eng.,  Nov.  7;   1907. 
Cartelli,  Lond.  Elec.,  62,  609;   1909. 


CHAPTER  IX. 

THEORY  OF  THE  ELECTRIC  ARC. 

UNTIL  the  ionic  theory  of  discharge  through  gases  was 
developed,  there  was  no  explanation  of  the  phenomena  of 
the  electric  arc  which  was  of  value.  But  in  recent  years 
several  explanations  based  on  this  theory  have  been  sug- 
gested and  an  outline  of  these  will  be  given  in  the  following 
pages.  The  first  attempt  in  this  direction  was  made  by 
the  present  writer  in  igoo.1  A  few  years  later  a  more 
complete  explanation  was  given  by  Stark,2  and  a  slightly 
different  one  by  Sir.  J.  J.  Thomson.3 

All  of  these  explanations  assume  that  the  current  is 
carried  by  ions  and  a  discussion  of  them  will  require  us  to 
understand,  first,  what  is  meant  by  ions;  second,  how  they 
are  produced;  and  third,  their  effect  on  the  potential 
gradient  between  two  electrodes,  especially  in  a  place  where 
ions  of  one  kind  only  exist. 

Definition  of  Ions  and  Electrons.  —  Certain  causes  ap- 
pear to  break  atoms  into  parts,  one  part  of  each  atom  being 
charged  positively  and  one  part  negatively.  These  parts 
have  been  called  ions.  They  tend  to  attach  themselves 
to  uncharged  atoms,  and  these  clusters  of  atoms  are  also 
called  ions,  so  that  an  ion  may  be  defined  as  an  atom,  a 
part  of  an  atom  or  a  cluster  of  atoms  which  has  a  positive 

1  Phys.  Rev.,  10,  151;  1900. 

2  Ann.  d.  Phys.,  12,  673;  1903. 

3  Conduction  of  Electricity  through  Gases,  ist.  Ed.,  p.  416. 

156 


THEORY  OF  THE   ELECTRIC  ARC  157 

or  negative  charge.  From  the  derivation  of  the  word,  it 
signifies  moving,  and  the  name  is  applied  to  nearly  anything 
that  will  move  in  an  electric  field  and  is  too  small  to  have 
any  other  name. 

This  definition  includes  ions  in  liquid  solutions,  but  in 
this  discussion  we  shall  consider  only  the  ones  which  are 
found  in  gases.  These  have  different  properties  from  those 
of  electrolytes  and  the  phenomena  of  the  arc  are  not  the 
same  as  those  existing  when  a  current  of  electricity  passes 
through  a  liquid.  These  differences  can  be  better  under- 
stood after  the  facts  relating  to  the  arc  have  been  more 
fully  discussed. 

The  movement  of  the  ions  constitutes  a  current  of  elec- 
tricity. Ions  thus  render  the  space  where  they  exist  con- 
ducting, and  by  this  means  their  presence  is  ordinarily 
detected. 

The  negative  part  which  is  broken  off  from  an  atom  or 
molecule  is  much  smaller  than  the  remaining  positive  part. 
This  ion  which  is  a  small  fraction  of  an  atom  is  often  called 
an  electron.  This  very  quickly  becomes  attached  to  an 
atom  or  molecule,  and  though  it  is  still  an  ion,  it  is  no 
longer  called  an  electron.  An  electron,  then,  is  a  negative 
ion  which  has  a  mass  very  much  smaller  than  that  of  an 
atom.  In  some  cases  of  discharge  through  gases  nearly 
all  of  the  negative  ions  are  electrons.  Cathode  rays,  for 
example,  are  streams  of  such  parts  of  atoms.  In  other 
cases  the  electrons  so  quickly  combine  with  molecules  that 
their  presence  can  scarcely  be  detected,  as  when  discharge 
in  air  at  atmospheric  pressure  is  produced  by  Rontgen 
rays.  In  discharge  through  hot  flames  there  are  probably 
present  in  large  numbers  both  electrons  and  negative  ions 
of  atomic  size. 


158  THE   ELECTRIC  ARC 

Causes  Producing  Ions.  —  Ions  thus  formed  do  not  con- 
tinue indefinitely.  They  quickly  recombine  and  again 
form  uncharged  atoms.  Thus,  to  have  a  continuous  supply 
of  ions,  there  must  be  a  continuous  production.  Among 
the  causes  producing  them  may  be  mentioned  radio-active 
substances,  Rontgen  rays,  ultra-violet  light,  the  impact  of 
ions  on  atoms,  chemical  action,  especially  at  high  tem- 
peratures, and  incandescent  solids.  Of  these,  two  only 
will  be  of  interest  to  us  at  this  time,  namely,  the  impact 
of  ions  on  atoms,  and  incandescent  solids. 

lonization  by  Impact.  —  Let  us  first  consider  ionization 
by  impact.  If  ions  exist  where  there  is  an  electric  field 
they  tend  to  move  with  an  accelerated  velocity.  Under 
ordinary  conditions,  they  can  move  but  a  short  distance 
before  colliding  with  an  atom  or  molecule  of  gas.  If  the 
atom  or  molecule  is  hit  with  sufficient  velocity,  it  is  broken 
into  parts  which  are  charged  and  which  are  indeed  new  ions. 
Thus,  cathode  rays  and  the  electrons  produced  by  ultra- 
violet light  or  incandescent  solids  ionize  the  gas  through 
which  they  pass  and  render  it  conducting.  It  has  been 
shown  by  Townsend  that  positive  ions  will  produce  the 
same  effect.1 

The  velocity  of  an  ion  at  any  instant  depends  on  the 
force  which  has  been  acting  on  it  and  upon  the  distance 
covered  since  its  last  collision,  or  in  other  words  upon  the 
potential  difference  through  which  it  has  passed  since  it 
was  at  rest.  Consequently,  to  have  sufficient  velocity  to 
ionize  by  impact,  an  ion  must  pass  through  a  certain 
potential  difference.  If  the  mean  free  path  is  too  short, 
or  the  electric  force  too  small,  no  effect  will  be  produced. 
The  measurements  made  by  Townsend  indicate  that  the 
i  Phil.  Mag.,  (6),  6,  598;  1903. 


THEORY  OF  THE   ELECTRIC  ARC 

negative  ion  must  pass  through  25  volts  in  order  to  ionize 
in  air,  and  the  positive  ion  must  pass  through  70  volts.1 
Davis2  gives  11.7  volts  as  the  value  needed  to  ionize  with 
the  negative  ions. 

The  ions  can  also  ionize  when  they  hit  the  molecules  of 
a  solid,  as  when  the  negative  ions  hit  the  surface  of  the 
anode,  or  the  positive  ones  hit  that  of  the  cathode.  The 
potential  difference  needed  in  this  case  is  greater  than  that 
needed  with  the  molecules  of  a  gas.  Thus  when  the  posi- 
tive ions  hit  a  cold  cathode,  they  need  to  pass  through  at 
least  300  volts  in  order  to  produce  electrons.  The  poten-, 
tial  difference  needed  by  the  negative  ions  is  not  so  well 
known,  but  it  is  probably  about  the  same  as  the  anode 
drop  of  the  unstriated  discharge  in  a  vacuum  tube  which 
is  approximately  20  volts.3 

lonization  by  Hot  Solids.  —  It  has  long  been  known  that 
substances  at  a  high  temperature  discharge  electrified 
bodies,  and  in  recent  years  it  has  been  shown  that  the  rate 
of  such  discharge  may  be  very  large.  This  was  shown  by 
Richardson  in  i9034  when  a  hot  wire  which  was  charged 
negatively  was  placed  in  a  vacuum.  A  little  later  Wehnelt 5 
found  that  the  discharge  from  some  of  the  oxides,  as,  for 
example,  calcium  oxide,  was  very  much  greater  than  that 
from  a  metal. 

It  was  believed  by  Richardson  that  this  discharge  was 
caused  by  electrons  coming  from  within  the  metal  and 
passing  through  its  surface  because  of  the  great  velocity 
which  they  have  at  high  temperatures,  and  he  derived  the 

1  Phil.  Mag.,  (6),  5,  395,  and  (6),  6,  613;  1903. 

2  Phys.  Rev.,  24,  102;  1907. 

3  Wied.  Ann.,  68,  752;  1899. 

4  Phil.  Trans.,  201  A,  497;  1903. 
6  Ann.  d.  Phys.,  14,  439;  1904, 


160  THE   ELECTRIC  ARC 

formula  /  =  AeQ\  where  /  is  the  current  passing  from  the 
metal,  0  the  absolute  temperature,  and  A  and  Q  are  con- 
stants, depending  on  the  kind  of  metal  used.  There  are 
somewhat  serious  objections  to  the  assumptions  made  by 
Richardson  in  deriving  this  formula,1  but  the  formula  itself 
has  been  found  to  be  approximately  true  for  several  of  the 
metals  and  will  give  an  idea  of  the  rapidity  with  which  the 
current  increases  when  the  temperature  is  raised. 

Fall  of  Potential  through  the  Arc.  —  To  pass  then  to 
the  arc,  we  have  found  that  it  may  be  divided  into  three 

parts,  the  part  near  the 
anode,  A,  Fig.  57.  at  which 
_  there  is  a  sudden  drop  in 
potential,  as  is  shown  in 
the  diagram;  that  through 
the  arc,  where  the  fall  in 
potential  is  gradual  and 
nearly  uniform,  as  ac\  and 

that  very  near  the  cathode,  C,  at  which  the  drop  is  again 
sudden. 

To  understand  these  peculiarities  we  may  begin  with  the 
case  where  ionization  is  produced  in  the  gas  between  the 
two  electrodes,  but  not  in  their  immediate  neighborhood; 
we  may  next  consider  the  phenomena  introduced  by  the 
impact  of  the  ions  on  the  electrodes,  and  finally  may  pass 
to  the  case  where  the  electrodes  are  incandescent. 

An  example  of  the  first  will  be  found  when  two  plates 
are  placed  on  opposite  sides  of  a  flame  and  at  some  distance 
from  it.  For  example,  let  ac,  in  Fig.  58,  be  a  space  where 
ionization  occurs.  This  space  will  then  contain  both  posi- 

1  Wilson,  Phil.  Trans.,  202  A,  243;  1904. 
Horton,  Phil.  Trans.,  207  A,  163;  1908. 


THEORY  OF  THE   ELECTRIC  ARC 


161 


FIG.  58. 


tive  and  negative  ions.  The  space  A  a  will  contain  only 
negative  ions  and  Cc  only 
positive  ions.  Where  there 
are  ions  of  one  sign  only,  the 
potential  gradient  changes  rap- 
idly and  the  drop  in  potential 
in  the  immediate  neighborhood 
of  A  and  C  may  become 
very  large.  The  mathemati- 
cal treatment  of  this  proceeds 
easily  in  simple  cases  from  the  equation 

dW  ,  dW  .  d2V 

TT  +  Tl    '  "71  =  —  4KP- 
dx2       dy2       dz2 

For  example,  when  the  lines  at  A,  a,  c,  C  represent  infinite 

planes,  V2>  — — »  where  b  is  the  distance  Aa,  V 

k 

the  change  in  potential  through  Aa,  k  the  velocity  of  the 
ions  per  unit  electric  force  and  i  the  current  per  unit  cross 
section.  The  units  used  are  volts,  amperes,  centimeters 
and  seconds.1  Thus  if  i  equals  io~8  amperes,  b  equals 
i  cm.,  and  k  equals  10,  then  V  is  greater  than  100  volts. 

lonization  at  Surface  of  Cathode,  with  Discharge  at  Low 
Pressure.  —  This  discussion  applies  also  to  the  case  where 
ionization  is  produced  by  impact,  as  with  discharge  through 
a  vacuum  tube.  But  here  a  complication  is  introduced. 
If  no  electrons  come  from  C,  all  those  between  the  plates 
will  soon  pass  to  A.  Let  us  suppose  that  the  region  Cc 
has  thus  been  cleared  of  negative  ions.  There  will  then 
be  a  large  drop  in  potential  here,  since  the  positive  ions 
will  have  moved  into  this  region  and  there  is  always  a  large 

1  Phys.  Rev.,  12,  79;  1901. 


1 62  THE  ELECTRIC  ARC 

drop  in  potential  in  a  region  where  there  is  only  one  kind 
of  ions.  If  this  drop  is  sufficiently  large,  the  positive  ions 
will  attain  high  velocities,  and  by  impact  on  the  boundary 
surface  at  C  they  also  will  ionize.  We  shall  then  have  a 
two-sided  action.  The  negative  ions  coming  from  C  will 
ionize  in  the  space  ac  and  the  positive  ions  from  ac  will 
ionize  at  C. 

As  the  negative  ions  thus  formed  begin  to  fill  the  space 
Cc,  the  drop  in  potential  will  become  smaller.  If,  however, 
it  becomes  small  enough,  ionization  at  C  will  cease  and 
the  potential  difference  will  again  become  greater.  For  a 
condition  of  equilibrium  the  potential  difference  must  be 
large  enough  so  that  positive  ions  will  ionize  at  C. 

Ionization  at  Surface  of  Anode.  —  We  find  that  the  phe- 
nomena at  the  anode  are  similar  to  those  at  the  cathode. 
The  essential  difference  is  that  the  negative  ions  ionize  by 
impact  much  more  easily  than  the  positive.  The  drop  in 
potential  at  the  anode  is  consequently  less  than  that  at  the 
cathode.  If  no  ions  came  from  the  anode,  there  would  be 
a  large  drop  in  potential  near  it,  as  in  the  corresponding 
case  with  the  cathode.  This  would  cause  the  negative  ions 
to  move  with  great  velocity  and  their  bombardment  of  the 
surface  layer  at  A  would  produce  new  ions.  As  before,  a 
condition  of  equilibrium  exists  when  the  drop  in  potential 
is  sufficiently  large  to  cause  many  of  the  negative  ions  to 
produce  new  ions  at  the  boundary  surface. 

Ionization  at  Cathode  of  Arc.  —  The  arc  is  in  many  ways 
similar  to  the  discharge  in  a  vacuum  tube.  There  is  a  drop 
in  potential  at  the  anode,  a  gradual  fall  through  the  gas  and 
another  sudden  drop  at  the  cathode.  The  essential  differ- 
ences between  the  two  phenomena  are  that  in  the  arc  the 
drop  in  potential  at  the  cathode  is  much  smaller  than  it  is 


THEORY  OF  THE  ELECTRIC  ARC  163 

in  a  Crookes'  tube  and  the  cathode  itself  must  be  very  hot. 
In  the  arc  the  cathode  drop  instead  of  being  300  volts  may 
be  as  low  as  5  volts  (p.  96).  That  the  cathode  must  be  hot 
was  shown  by  Luggin 1  who  found  that  a  carbon  disk  kept 
cool  by  being  rotated  could  be  used  as  the  anode,  but  not 
as  the  cathode  of  the  arc.  Stark  and  Cassuto2  showed  the 
same  thing  for  a  metal  kept  cool  by  being  rotated,  and  for 
an  electrolyte  which  can  never  be  raised  to  a  high  tem- 
perature. In  some  work  by  the  present  writer3  it  was  found 
that  the  anode  end  of  an  arc  in  a  vacuum  could  easily  be 
made  to  jump  to  a  carbon  electrode  placed  near  the  arc, 
but  that  the  cathode  end  could  not  be  made  to  do  so,  except 
when  the  pencil  was  white  hot. 

Assumption  that  the  Electrons  are  from  Within  the 
Cathode.  —  As  a  result  of  this  fact  all  agree  in  assuming 
that  the  production  of  the  ions  at  the  cathode  is  the  basis 
of  any  explanation  of  the  arc.  They  differ,  however,  as 
to  how  these  ions  are  produced.  According  to  one  view 
the  cathode  is  heated  by  the  impact  on  it  of  positive  ions, 
until  it  becomes  sufficiently  hot  to  send  out  ions  from 
within  the  solid  to  the  surrounding  gas,  as  in  experiments 
performed  with  hot  platinum  wires.  According  to  the 
other  view  the  electrons  are  produced  by  the  impact  of  the 
positive  ions  on  the  molecules  at  the  surface  of  the  cathode, 
and  the  cause  for  the  small  cathode  drop  is  the  fact  that 
ionization  occurs  very  much  more  easily  when  the  surface 
of  the  cathode  is  at  a  high  temperature.  Both  Stark  and 
Thomson  have  made  the  former  assumption  the  basis  of 
their  explanations.  They  suppose  the  hot  cathode  to  be 
the  origin  of  the  negative  ions  and  that  the  rise  in  potential 

1  Wien.  Sitzungber.,  96,  2  A,  767;  1887.  2  Phys.  ZS.,  5,  264;  1904. 

3  Phys.  Rev.,  19,  119;  1904. 


1 64  THE  ELECTRIC  ARC 

need  be  only  great  enough,  so  that  the  positive  ions  by 
their  bombardment  of  the  cathode  should  raise  it  to  the 
necessary  temperature. 

There  are,  however,  objections  to  this  view.  The  most 
important  of  these  is  that  there  are  many  substances  which 
can  be  used  as  the  cathode  of  an  arc  and  yet  melt  and 
vaporize  before  a  temperature  is  reached  at  which  negative 
ions  are  given  off.  The  most  noteworthy  example  of  this 
occurs  with  the  arc  between  mercury  terminals.  Mercury 
vaporizes,  especially  in  a  vacuum,  at  temperatures  far 
below  that  at  which  negative  ions  pass  from  a  metal. 

In  reply  to  this  last  objection  it  was  shown  by  Stark1 
that  even  in  the  case  of  mercury  there  is  a  point  at  the 
cathode  which  is  very  hot  and  at  this  point  there  is  a  con- 
tinuous spectrum.  This  fact  was  also  pointed  out  by 
Arons.2  Apparently  the  rise  in  temperature  occurs  so 
suddenly  that  the  mercury  does  not  become  a  gas  until 
after  the  atoms  are  set  in  such  violent  vibration  that  they 
give  out  light. 

If  we  should  assume  that  this  difficulty  may  be  thus 
explained,  there  is  still  the  fact  that  in  a  vacuum  the  metals 
which  melt  the  most  easily  can  be  made  the  cathode  of  the 
arc,  while  those,  like  iron  and  copper,  which  do  not  melt 
easily  can  not  be  so  used.  We  should  expect  that  iron 
would  give  off  ions  at  least  as  readily  as  mercury,  if  the 
phenomenon  depended  only  on  raising  the  metal  to  a  high 
temperature. 

There  are  also  certain  minor  difficulties  met  with  in  this 
explanation.  For  example,  the  measurements  made  by 
Richardson  on  the  discharge  from  hot  carbon 3  would  indi- 

1  Physik.  ZS.,  5,  75°;  1904.  2  Wied.  Ann.,  58,  89;  1896. 

3  Phil.  Trans.,  201  A,  497;  1903. 


THEORY  OF  THE  ELECTRIC  ARC  165 

cate  that  at  3140°  C.,  which  is  the  temperature  of  the 
cathode  according  to  Reich,1  the  rate  of  discharge  from  the 
cathode  should  be  2  X  io8  amperes  per  sq.cm.,  whereas 
the  measurements  which  Reich  made  on  the  size  of  the 
cathode  spot  indicate  that  the  current  is  but  318  amperes 
per  sq.  cm. 

Second  Explanation  of  lonization  at  Cathode.  —  Accord- 
ing to  a  second  explanation  the  ionization  at  the  cathode  is 
produced  by  the  impact  of  the  positive  ions  on  its  surface. 
In  the  discharge  from  a  cold  cathode  such  ionization  is 
supposed  to  occur  and  the  only  objection  to  assuming  that 
it  occurs  at  the  cathode  of  the  arc  is  that  the  cathode  drop 
is  here  much  smaller.  However,  it  has  been  shown  by 
Hittorf 2  and  Cunningham3  that  the  cathode  drop  becomes 
smaller  as  the  temperature  of  the  cathode  is  raised.  The 
same  occurrence  has  been  found  when  using  hot  calcium 
oxide  for  the  cathode.4  It  would  in  fact  be  surprising  if 
it  were  not  much  easier  to  ionize  molecules  which  are  at  the 
temperature  of  the  arc,  since  even  without  impact  they 
emit  some  electrons. 

Almost  conclusive  evidence  in  favor  of  this  view  is  given 
by  the  similarity  between  the  glow  discharge  in  a  partial 
vacuum,  the  luminous  discharge  from  hot  calcium  oxide, 
and  the  arc,  since  with  the  first  two  of  these  we  certainly 
have  ionization  at  the  cathode  produced  by  impact  of 
positive  ions.  The  similarity  between  these  is  shown  by 
the  fact  that  it  is  quite  possible  to  pass  by  gradual  changes 
from  the  ordinary  form  of  discharge  in  a  vacuum,  where 
the  cathode  drop  must  be  several  hundred  volts,  through 
the  discharge  from  a  heated  cathode,  where  Cunningham 

1  Phys.  ZS.,  7,  73;  1906.  3  Phil.  Mag.,  (6),  9,  202;  1905. 

2  Wied.  Ann.,  21,  133;  1884.  4  Phys.  Rev.,  32,  507;  1911. 


166  THE  ELECTRIC  ARC 

found  it  to  be  250  volts,  to  that  from  hot  lime,  where  it 
varies  from  70  to  12  volts,  and  then  to  the  arc,  where  it 
may  be  as  low  as  6  volts.  The  luminous  discharge  from 
hot  calcium  oxide  is  identical  with  the  arc  in  a  vacuum, 
except  that  with. the  arc  no  independent  source  of  energy 
is  needed  to  heat  the  cathode1  and  this  is  a  thing  which  has 
nothing  to  do  with  the  manner  in  which  the  ions  are  pro- 
duced. 

That  there  is  ionization  by  impact  at  the  cathode  with 
the  luminous  discharge  from  hot  calcium  oxide  is  shown 
by  the  following.  With  hot  calcium  oxide  it  is  possible 
to  have  a  very  small  non-luminous  discharge  and  with  the 
same  current  heating  the  cathode  and  the  same  potential 
difference  between  the  electrodes  to  have  a  large  luminous 
discharge,  providing  the  discharge  has  momentarily  been 
raised  to  an  amount  sufficiently  high  to  start  the  larger  dis- 
charge. The  number  of  electrons  emitted  from  within 
the  calcium  oxide  can  not  be  greatly  different  in  the  two 
cases,  for  the  temperature  of  the  cathode  has  not  appre- 
ciably changed,  and  a  study  of  the  potential  between 
electrodes  shows  that  the  increase  in  current  can  not  be 
due  to  a  movement  of  the  positive  ions  toward  the  cathode. 
The  only  way  to  explain  the  increase  is  by  assuming  that 
in  the  second  form  of  discharge  a  greater  number  of  elec- 
trons is  produced  at  the  cathode  by  the  impact  of  a  greater 
number  of  positive  ions.  The  appearance  of  the  rays 
streaming  from  the  cathode  confirms  this  view.  If  then 
we  have  ionization  by  impact  with  hot  calcium  oxide,  we 
undoubtedly  have  the  same  manner  of  ionization  in  the  arc. 

Causes  Determining  the  Amount  of  the  Cathode  Drop.  — 
The  immediate  cause  of  the  drop  in  potential  at  the  cathode 
1  Phys.  Rev.,  19,  361;  1909. 


THEORY  OF  THE  ELECTRIC  ARC 

is  the  accumulation  in  its  neighborhood  of  positive  ions 
which  have  been  drawn  from  .the  vapor  of  the  arc  but  have 
not  yet  reached  the  cathode.  This  accumulation  can  not 
become  indefinitely  great,  for,  when  it  increases,  the  current 
flowing  from  the  cathode  increases,  and  this  soon  causes 
the  drop  in  potential  through  the  remainder  of  the  circuit 
to  become  as  great  as  it  is  possible  to  have  it  with  the  given 
E.M.F.  On  the  other  hand  the  cathode  drop  can  not  fall 
below  a  certain  value,  for  it  must  be  great  enough  both 
to  cause  negative  ions  to  be  formed  at  the  cathode  and  to 
cause  these  to  produce  positive  ions  by  their  impact  on 
the  molecules  of  the  gas.  Whichever  of  these  is  the  greater 
will  determine  how  great  the  cathode  drop  must  be. 

One  can  not  at  present  say  with  certainty  which  of  these 
is  the  greater.  The  cathode  drop  in  some  cases  is  not  only 
much  smaller  than  that  needed  to  produce  electrons  by 
the  impact  of  the  positive  ions  on  a  cold  cathode,  but  also 
much  smaller  than  that  needed  to  produce  positive  ions  by 
the  impact  of  electrons  on  the  molecules  of  a  gas.1  Appar- 
ently at  high  temperatures  both  forms  of  ionization  occur 
much  more  easily  than  at  low.  Since  we  do  not  know  the 
exact  relation  between  the  temperature  and  the  potential 
difference  needed  for  ionization  with  either  the  positive 
or  negative  ions,  we  can  not  state  definitely  which  is  the 
lower  at  high  temperatures. 

There  are,  however,  reasons  for  believing  that  in  all  cases 
the  potential  difference  needed  for  ionization  by  the  posi- 
tive ions  is  the  greater.  We  shall  find,  for  example,  when 
we  examine  the  drop  in  potential  through  the  gas  of  the 
arc,  that  in  some  way  the  ionization  of  the  arc  is  kept  up, 
though  the  mean  free  path  of  the  electrons  in  some  cases 

1  Phys.  Rev.,  24,  93;  1907. 


1 68  THE   ELECTRIC  ARC 

is  through  not  more  than  0.03  volt.  If  ionization  by  the 
electrons  coming  from  the  cathode  can  be  produced  by 
anything  like  this  potential  difference,  then  the  drop  which 
we  actually  find  at  the  cathode  must  be  determined  by  the 
potential  difference  needed  for  ionization  with  the  positive 
ions  and  not  by  that  needed  for  the  negative  ones. 

Ionization  at  the  Anode.  —  There  are  two  distinct  sets  of 
conditions  to  be  found  at  the  anode,  depending  on  whether 
the  cathode  rays  hit  directly  on  the  anode  or  not.  The 
first  conditions  exist  only  when  the  arc  is  in  a  very  high 
vacuum.  The  negative  ions  then  go  directly  from  the 
cathode  to  the  anode.  There  is  then  no  luminosity  between 
the  electrodes  which  is  at  all  comparable  with  that  ordi- 
narily existing  in  the  arc  and  there  is  apparently  but  very 
slight  ionization  of  the  gas  between  the  electrodes. 

In  all  probability  there  is  then  no  ionization  at  the 
surface  of  the  anode.  Apparently  the  conditions  are 
identical  with  those  in  a  vacuum  tube  with  currents  such 
as  were  studied  by  Skinner1  and  by  myself.2  In  these 
investigations  it  was  found  that  the  anode  drop  varied 
from  one  or  two  volts  to  over  one  hundred  volts.  It  appar- 
ently depended  on  the  average  velocity  of  the  negative  ions 
when  they  reached  the  anode,  the  anode  drop  decreasing 
as  the  velocity  of  the  ions  increased.  This  is  what  would 
be  expected  if  the  current  near  the  anode  is  carried  by  ions 
of  one  sign  only  as  is  shown  on  page  161. 

Whether  this  is  the  whole  explanation  of  the  anode  drop 
with  the  arc  in  a  vacuum  under  very  low  pressure  is,  no 
doubt,  open  to  question.  The  fact  that  Stark,  Retschinsky, 
and  Schaposchnikoff 3  found  that  it  was  nearly  independent 

1  Phil.  Mag.,  (6),  2,  637;  1901.       2  Phys.  Rev.,  29,  351;  1909. 
3  Ann.  d.  Phys.,  18,  244;  1905, 


THEORY  OF   THE  ELECTRIC  ARC 

of  the  current  under  these  conditions  would  indicate  that 
it  is  not,  but  it  is  doubtful  whether  any  more  complete 
explanation  can  be  given  until  some  method  is  found  for 
determining  the  velocity  of  the  negative  ions  when  in  the 
immediate  neighborhood  of  the  anode. 

Ordinarily  the  ions  are  stopped  before  reaching  the  anode 
and  we  then  have  the  second  set  of  conditions;  namely, 
those  which  occur  when  there  is  a  large  amount  of  ioniza- 
tion  and  of  luminosity  between  the  electrodes.  Under 
these  conditions  there  is  ionization  at  the  anode.  If  there 
were  not,  the  drop  would  be  very  much  larger  than  it  is. 

The  amount  of  the  anode  drop  under  such  conditions 
appears  to  be  determined  by  the  potential  difference  neces- 
sary to  produce  ionization  at  the  surface  of  the  anode. 
That  is,  the  drop  increases  until  it  becomes  sufficiently 
large  to  cause  the  negative  ions  by  their  impact  to  disrupt 
the  atoms  at  the  surface  of  the  anode.  Of  these  new  atoms 
the  positive  ones  move  toward  the  cathode  and  by  their 
electrostatic  influence  keep  the  potential  difference  from 
becoming  any  larger. 

The  phenomenon  is  much  the  same  at  the  anode  as  at 
the  cathode,  ionization  at  the  anode  being  produced  by  the 
impact  of  the  negative  ions,  and  that  at  the  cathode  by 
the  impact  of  the  positive  ones.  It  is  not  necessary,  how- 
ever, for  the  temperature  of  the  anode  to  be  high,  while  it 
is  necessary  that  the  cathode  should  be  very  hot.  More- 
over at  the  cathode  there  is  a  production  of  negative  ions 
at  the  surface  and  of  positive  ones  at  a  short  distance  from 
it,  while  the  positive  ions  produced  at  the  anode  play  no 
part  in  the  production  of  negative  ones. 

This  view  is  in  harmony  with  the  fact  that  the  anode 
drop  is  nearly  independent  of  the  amount  of  the  current. 


170  THE  ELECTRIC  ARC 

The  same  reasoning  that  was  given  in  connection  with  the 
cathode  drop  would  apply  here.  Whether  the  number  of 
negative  ions  going  to  the  anode  is  large  or  small,  a  new 
ion  must  be  formed  for  each  negative  ion  coming  to  the 
anode,  and  a  definite  potential  difference  is  needed  for  this 
purpose. 

The  view  was  expressed  by  Sir.  J.  J.  Thomson1  that  the 
ionization  at  the  anode  is  caused  by  the  anode  being 
heated  to  a  high  temperature  and  that  the  anode  drop  is 
determined  by  the  amount  of  energy  necessary  to  keep  the 
anode  at  this  temperature.  However,  there  are  many 
forms  of  the  arc  where  the  anode  is  not  raised  to  a  tem- 
perature which  can  be  considered  high,  so  that  the  anode 
drop  would  not  appear  to  be  determined  by  such  a  require- 
ment. 

Blondel2  expresses  the  view  that  when  the  anode  is 
vaporized  it  gives  out  positive  ions.  I  have  not  been  able 
to  find  anything  that  confirms  this  view  and  the  fact  that 
the  anode  drop  in  a  mercury  arc  is  much  the  same  with  a 
mercury  anode  which  is  easily  vaporized  as  it  is  with  an 
iron  anode  which  is  not  vaporized  would  seem  to  make 
this  view  untenable. 

Discharge  of  Ions  to  Electrodes.  —  We  have  considered 
the  manner  of  production  of  ions  at  the  electrodes,  but  it  is 
also  true  that  the  ions  coming  to  them  must  in  some  way 
lose  their  charge.  Whether  the  charge  is  detached  from 
the  ion  and  given  to  the  electrode  or  is  neutralized  by 
some  charge  coming  from  the  electrode,  we  do  not  know, 
but  in  either  case  it  is  hardly  to  be  expected  that  the  action 
will  take  place  without  loss  or  gain  of  energy.  That  it  does 

1  "  Conduction  of  Electricity  through  Gases,"  ist  ed.,  p.  424. 

2  Trans.  Inter.  Elec.  Cong.,  St.  Louis,  2,  747, 1904. 


THEORY  OF  THE   ELECTRIC   ARC 

not  happen  without  complicating  action  when  cathode 
rays  strike  an  anti-cathode  is  evident,  for  we  there  have 
secondary  rays  given  off  and  also  a  large  development  of 
heat.  As  far  as  the  writer  is  aware  there  has  been  no  work, 
either  experimental  or  theoretical,  done  on  this  subject  in 
the  case  of  the  arc. 

lonization  of  the  Gas  between  Electrodes.  —  With  very 
low  pressures  the  current  is  carried  almost  entirely  by 
electrons  which  appear  as  cathode  rays  streaming  out 
toward  the  anode.  These,  no  doubt,  ionize  the  gas  through 
which  they  pass.  The  ability  to  ionize  the  gas  is  one  of  the 
well-known  properties  of  such  rays  and  certainly  ionization 
of  the  gas  must  be  produced  in  some  way,  since  positive 
ions  come  from  the  gas  and  heat  the  cathode. 

As  the  pressure  of  the  gas  or  as  the  distance  between  the 
electrodes  is  increased,  a  glow  appears  at  the  anode.  Under 
some  conditions  striations  appear  as  was  shown  in  Fig.  20. 
Ordinarily  with  increase  of  pressure  there  is  a  continuous 
glow  between  the  electrodes.  Increasing  the  pressure 
further  does  not  change  the  character  of  this  glow,  except 
to  make  it  more  intense. 

With  this  form  of  the  arc  it  is  also  certain  that  there 
is  ionization  between  the  electrodes.  In  air,  for  example, 
the  electrons  coming  from  the  cathode  can  not  go  far 
before  being  stopped  by  collision  with  the  molecules  of  the 
air  and  recombination  between  the  ions  must  take  place 
in  many  cases.  If  so,  there  must  also  be  fresh  ionization 
to  keep  up  the  supply  of  ions. 

Moreover  we  know  that  positive  ions  are  produced  in 
the  gas,  since  they  are  continually  moving  toward  the 
cathode,  as  is  shown  by  the  potential  gradient  between 
the  electrodes.  This  gradient  has  been  found  in  all  cases 


172  THE  ELECTRIC  ARC 

to  be  practically  uniform,  which  could  not  be,  if  there  were 
not  an  equal  number  of  positive  and  negative  ions  through 
the  gas. 

This  ionization  is  no  doubt  produced  by  the  impact  of 
electrons  on  the  atoms  or  molecules.  It  would  seem  at 
first  as  if  there  were  other  possible  explanations  for  the 
ionization.  It  has  been  shown,  for  example,  that  ultra- 
violet light  ionizes  gases.1  Light  of  the  short  wave  length 
needed  to  produce  such  ionization  is  not  known  to  exist 
in  any  of  the  forms  of  the  arc,  but  since  it  is  completely 
absorbed  by  a  thin  layer  of  air,  it  is  quite  possible  that  it 
has  been  overlooked  and  does  indeed  exist  in  all  forms  of 
the  arc. 

Such  light  may  indeed  be  an  aid  in  producing  ionization, 
but  it  can  not  be  the  only  source,  for  it  comes  only  from 
vibrating  ions,  and  its  energy  comes  from  the  energy  given 
to  a  system  of  ions  when  the  molecule  is  broken  into  two 
parts.  The  energy  of  vibration  of  one  pair  of  ions  will 
not  be  sufficient  to  set  another  pair  into  similar  vibration 
of  equal  intensity,  for  a  large  amount  of  this  energy  is  being 
continually  radiated  away  from  the  arc  and  another  large 
part  is  changed  into  heat  and  conducted  away,  and  it  would 
require  all  of  the  energy  of  one  vibration  to  produce  an- 
other like  it.  The  number  of  vibrating  atoms  will,  there- 
fore, diminish,  or  some  other  source  of  energy  must  be 
changed  into  that  of  vibration.  In  other  words,  if  the 
number  of  vibrating  ions  is  to  be  kept  constant  the  elec- 
trical energy  must  in  some  way  be  changed  into  that  of 
ultra-violet  light,  and  the  only  known  way  for  this  to  be 
done  in  a  gas  is  by  impact  of  the  ions  on  the  molecules. 

The  same  kind  of  reasoning  will  show  that  it  is  not 
1  Phys.  Rev.,  32,  i;  1911. 


THEORY  OF  THE  ELECTRIC  ARC 

possible  for  any  other  kind  of  radiation,  such  as  Rontgen 
rays,  or  "entladungstrahlen"  to  be  the  sole  source  of  the 
ionization. 

On  the  other  hand  there  are  serious  objections  to  believing 
that  impact  of  ions  is  the  sole  cause  of  ionization.  The 
first  of  these  is  that  the  mean  free  path  of  the  electrons  is 
through  too  small  a  difference  of  potential  to  produce 
ionization.  The  work  of  Davis1  indicates  that  at  ordinary 
temperatures  the  ions  must  move  through  11.7  volts  in 
order  to  ionize.  We  may  get  some  idea  of  the  potential 
difference  through  which  the  electrons  in  the  arc  pass  by 
assuming  that  the  mean  free  path  of  the  ions  varies  in- 
versely as  the  density  of  the  gas,  that  the  electric  force  of 
the  arc  is  27  volts  per  centimeter,2  that  the  mean  free  path 
of  the  electrons  in  air  at  a  pressure  of  i  mm.  and  a  tempera- 
ture of  20°  C.  is  0.0475  cm.  as  found  by  Townsend,3  and 
that  the  temperature  of  the  gas  of  the  arc  is  3700°  C., 
the  temperature  of  the  anode  as  given  by  Waidner  and 
Burgess.4  The  mean  free  path  of  the  electrons  computed 
from  these  assumptions  is  through  a  potential  difference 
of  0.025  volt,  which  is  quite  different  from  11.7  volts,  the 
required  amount. 

In  the  second  place  the  electric  force  through  the  arc 
does  not  increase  in  inverse  proportion  to  the  length  of  the 
mean  free  path  of  the  ions,  as  it  should,  if  the  ions  are 
caused  by  the  impact.  Thus,  in  experiments  performed 
by  myself,  it  was  found  that  the  electric  force  in  the  arc 
between  two  solid  carbons  was  23.4  volts  per  centimeter 
when  the  pressure  was  730  mm.,  and  13.2  volts  with  a 
pressure  of  2  mm.  The  temperature  had  apparently 

1  Phys.  Rev.,  24,  93;  1907.  3  Phil.  Mag.,  (6),  I,  215;  1901. 

2  Mrs.  Ayrton's  "Electric  Arc,"  p.  231.       4  Phys.  Rev.,  19,  250;  1904. 


174  THE  ELECTRIC  ARC 

changed  but  little,  so  that  the  mean  free  path  in  this  last 
case  was  approximately  three  hundred  times  greater  than 
that  in  the  first,  while  the  electric  force  was  only  one-half 
as  great.  Again,  in  the  data  given  by  Knipp,  the  change 
in  the  electric  force  was  much  smaller  than  that  in  the 
pressure. 

It  has  been  suggested  by  the  author  that  these  diffi- 
culties can  be  easily  explained  if  we  assume  that  the  mole- 
cules of  a  gas  are  much  more  easily  ionized  when  the 
temperature  of  the  gas  is  high  than  when  low.1  We  have 
already  seen  that  the  molecules  on  the  surface  of  a  solid 
are  more  easily  broken  apart  if  the  solid  is  very  hot  and 
in  all  probability  the  same  thing  occurs  with  gases.  This 
explanation  seems  the  more  reasonable  since  the  gas  in  the 
arc  is  always  at  a  high  temperature.  Even  when  the 
pressure  of  the  gas  was  only  0.5  mm.,  the  temperature  of 
the  arc  between  carbons  was  sufficiently  high  to  melt 
platinum.  As  has  been  shown  there  is  a  difference  of 
opinion  regarding  the  mercury  arc,  but  it  seems  safe  to 
assume  that  its  temperature  is  at  least  high. 

Such  an  assumption  will  very  easily  explain  the  difficul- 
ties which  have  been  mentioned.  It  would,  for  example, 
explain  the  fact  that  the  larger  the  current  flowing  through 
the  arc  the  less  the  electric  force  required  to  produce  it,  for 
when  the  current  increases  there  is  an  increase  in  the  heat 
developed  in  the  arc,  and  if  ionization  occurs  more  easily 
at  high  temperatures,  then  the  electric  force  needed  to 
produce  the  greater  amount  of  ionization  may  remain 
nearly  constant  or  even  become  smaller. 

It  would  explain  the  phenomena  at  different  pressures. 
When  the  mean  free  path  of  the  ions  is  sufficiently  large, 
1  Phys.  Rev.,  19,  134;  1904. 


THEORY  OF  THE   ELECTRIC  ARC  175 

ionization  will  be  produced  without  high  temperature  and 
we  then  have  the  arc  at  lower  temperatures.  As  the  mean 
free  path  becomes  less,  the  average  velocity  of  the  ions 
becomes  less,  and  in  order  to  have  ionization,  the  tem- 
perature must  be  raised.  At  still  higher  pressures  the 
mean  velocity  of  the  ions  becomes  very  small  and  the  tem- 
perature is  the  determining  factor.  Then  it  makes  little 
difference  what  the  mean  free  path  of  the  ions  may  be,  if 
only  the  temperature  is  sufficiently  high. 

This  view  is  also  in  harmony  with  the  facts  observed  by 
Pollak.  The  mercury  vapor  above  the  arc  was  found  by 
him  to  be  but  slightly  conducting  when  the  current  passing 
through  it  was  small.  The  conductivity  was  found  to 
become  very  large  when  the  current  was  increased,  so  that 
a  considerable  amount  of  heat  was  developed. 

But  it  should  be  added  that  the  assumption  that  the 
ultra-violet  light  causes  the  molecules  to  become  more 
easily  ionized  by  impact  would  also  explain  any  difficulties. 
We  not  only  have  high  temperatures,  but  also  ultra-violet 
light  in  all  forms  of  the  arc.  This  is  especially  true  of  the 
mercury  arc,  where  ions  are  formed  with  exceptional  ease. 
Thus,  when  the  current  increases,  the  amount  of  this  light 
increases,  which  could  account  for  the  greater  ease  of 
ionization  with  larger  currents.  With  increase  in  pressure 
there  is  an  increase  in  the  voltage,  the  amount  of  energy 
used  in  the  arc  increases,  and  no  doubt  the  amount  of  ultra- 
violet light  also  becomes  greater,  which  would  account  for 
the  ionization  by  impact  regardless  of  the  small  difference 
of  potential  through  which  the  electrons  move. 

Thus,  either  of  these  explanations  would  seem  reasonable 
and  no  fact  is  known  to  the  writer  which  would  enable  one 
to  decide  between  them.  It  is  indeed  altogether  probable 


176  THE   ELECTRIC  ARC 

that  both  of  these  causes  may  aid  in  making  it  easier  for 
electrons  to  ionize  by  impact. 

We  may  then  sum  this  up  by  saying  that  the  direct  cause 
of  ionization  in  the  arc  is  the  impact  of  electrons  on  the 
molecules  of  the  gas  and  that  this  ionization  is  aided  either 
by  the  high  temperature  of  the  arc,  or  by  the  presence  of 
some  radiation,  such  as  ultra-violet  light,  or  by  both  of 
these. 

An  explanation  has  been  given  by  Sir  J.  J.  Thomson1 
for  the  large  discharge  passing  from  hot  calcium  oxide 
when  in  a  vacuum,  in  which  he  assumes  that  repeated  bom- 
bardment of  molecules  by  electrons  will  break  the  molecules 
apart,  even  when  one  impact  would  be  quite  unable  to  do 
so.  Evidently  the  same  explanation  could  be  given  for  the 
ionization  in  the  arc.  There  are,  however,  serious  ob- 
jections to  this  explanation  in  the  case  of  discharge  from 
hot  calcium  oxide2  and  until  further  evidence  is  found  in 
favor  of  that  view  it  would  seem  to  be  a  less  probable 
explanation  for  the  ionization  of  the  arc  than  that  which 
has  been  suggested. 

Velocity  of  the  Ions.  —  The  current  through  the  arc 
is  carried  very  largely  by  electrons.  These  move  much 
more  rapidly  than  positive  ions,  since  their  masses  are 
much  smaller,  while  their  charges  are  the  same.  We  do 
not,  however,  have  any  data  as  to  the  exact  values  of  the 
velocities  of  either  the  positive  or  negative  ions  in  the  arc. 
As  far  as  the  carbon  arc  is  concerned  we  do  not  have  any 
experiment  showing  definitely  whether  the  positive  or 
negative  ions  move  the  more  rapidly.  There  have  been 
several  different  methods  used  for  the  purpose  of  deter- 
mining this  question,  but  none  of  them  is  entirely  satis- 
1  Nature,  73,  495;  1906.  2  Phys.  Rev.,  32,  492;  1911. 


THEORY  OF   THE   ELECTRIC  ARC  177 

factory.  The  first  of  these  was  one  used  by  myself  where 
the  positive  ions  were  drawn  from  an  arc  by  a  charged 
cylinder  placed  about  the  arc.  In  this  experiment  the 
positive  ions  .were  found  to  have  a  greater  velocity  than 
the  negative  ones.1  However,  the  positive  ions  probably 
came  from  the  hot  positive  electrodes  and  showed  nothing 
concerning  the  ions  in  the  arc  itself.2 

That  this  is  the  correct  interpretation  appears  from  the 
work  of  Merritt  and  Stewart  who  showed  that  when  ions 
are  blown  from  an  arc  by  a  draft  of  air  and  their  velocities 
tested  a  few  centimeters  from  the  arc  the  negative  ions 
have  the  greater  velocities.3  The  same  thing  has  since  been 
shown  by  myself4  and  also  by  McClelland,5  who  be- 
lieved that  it  proved  that  the  negative  ions  had  the  greater 
velocity  not  only  outside  of  the  arc,  but  also  within  it. 

A  third  method  of  attacking  this  problem  was  given  by 
Swinton.6  In  his  experiment  one  of  the  carbons  was  hollow 
and  an  insulated  Faraday  cylinder  of  brass  was  placed 
within  this.  It  was  found  that  the  cylinder  became 
charged  positively  as  compared  with  the  electrode  in  which 
it  was  placed  when  this  was  the  cathode,  and  negatively 
when  it  was  the  anode,  and  that  the  negative  charge  was 
acquired  more  rapidly  than  the  positive.  From  this 
Swinton  concluded  that  the  negative  ions  moved  the  more 
rapidly.  However,  this  effect  might  easily  be  due  to  the 
fact  that  the  difference  of  potential  between  the  vapor  and 
the  anode  is  greater  than  that  between  the  vapor  and  the 
cathode.7 

1  Phys.  Rev.,  12,  137;  1901.  B  Proc.  Camb.  Phil.  Soc.,  10,  241;  1899. 

2  Phys.  Rev.,  15,  345;  1902.  6  Proc.  Roy.  Soc.,  76  A,  553;  1905. 

3  Phys.  Rev.,  7,  129;  1898.  7  Phys.  Rev.,  24,  506;  1907. 

4  Phys.  Rev.,  12,  147;  1901. 


178  THE  ELECTRIC  ARC 

Still  another  method  was  given  by  Stark,  Retschinsky, 
and  Schaposchnikoff.1  They  measured  the  drop  in  potential 
near  secondary  electrodes  placed  in  the  arc,  but  such 
measurements  in  the  carbon  arc  are  complicated  by  the 
high  temperatures  of  the  exploring  electrodes  and  by  the 
difference  of  potential  which  exists  between  such  electrodes 
and  the  surrounding  gas,  so  that  even  these  measurements 
can  not  be  considered  as  giving  a  definite  proof  of  the 
relative  velocities  of  the  negative  and  positive  ions  in  the 
carbon  arc. 

When  we  turn  to  the  mercury  arc  we  have  more  definite 
data.  The  measurements  of  Stark,  Retschinsky,  and 
Schaposchnikoff  were  here  made  with  cold  exploring  elec- 
trodes and  there  would  seem  to  be  no  question  but  that 
they  showed  that  the  negative  ions  had  the  greater  velocity. 
The  same  thing  was  shown  by  Schenkel  by  means  of  the 
Hall  effect  (p.  101),  although  the  values  given  by  him  to 
the  velocity  of  the  negative  ions  depended  on  certain 
appearances  which  are  not  sufficiently  definite  to  give 
exact  data. 

In  .addition  to  these  measurements  on  the  mercury  arc 
there  is  indirect  evidence  furnished  by  the  very  great 
velocity  of  the  negative  ions  in  the  discharge  from  hot 
platinum  and  from  hot  lime  in  a  vacuum  and  by  the  fact 
that  in  the  flame  where  the  temperature  is  still  much  lower 
than  in  the  arc  the  velocity  of  the  negative  ions  is  greater 
than  the  positive,  so  that  in  all  probability  in  all  forms 
of  the  arc  the  velocity  of  the  negative  ions  is  much  greater 
than  that  of  the  positive.2 

1  Ann.  d.  Phys.,  18,  230;  1905. 

2  Certain  theoretical  considerations  which  will  be  published  shortly  in 
the  Physical  Review  lead  to  the  same  conclusion. 


THEORY  OF  THE   ELECTRIC  ARC  179 

While  suggestions  have  thus  been  made  as  to  the  cause 
of  the  ionization  between  the  electrodes,  not  even  a  be- 
ginning has  been  made  toward  a  quantitative  analysis  of 
the  amount  of  the  electric  force.  Not  even  in  the  mercury 
arc  do  we  know  the  absolute  velocity  of  the  ions,  the  poten- 
tial difference  for  ionization  by  impact,  the  rate  of  recom- 
bination, or  the  mean  free  path  of  the  ions,  and  yet  all  of 
these  quantities  must  be  known  in  order  to  give  an  ex- 
planation of  the  magnitude  of  the  electric  force. 

Action  in  Arc  not  the  Same  as  in  an  Electrolyte.  —  It 
should  be  clearly  understood  that  the  explanations  here 
offered  are  not  in  any  way  based  on  the  idea  that  the  cur- 
rent in  the  arc  is  carried  by  particles  driven  off  from  the 
electrodes.  If  the  current  were  carried  by  particles  the 
spectrum  of  the  vapor  of  the  arc  would  be  a  continuous 
spectrum  instead  of  the  line  spectrum  which  is  actually  found. 

Neither  is  it  possible  that  the  current  is  carried  by  atoms 
or  molecules  driven  off  from  the  electrodes  as  in  electro- 
lytes. It  has  been  shown,  for  example,  by  Matthies1  that 
the  current  in  the  mercury  arc  is  carried  by  electrons  and 
not  by  charged  atoms.  Both  the  pressure  on  the  anode  and 
the  behavior  of  the  current  flowing  to  an  exploring  electrode 
placed  in  the  vapor  indicate  this. 

The  same  thing  is  shown  by  the  experiments  performed 
by  Weedon.2  He  found  that  a  copper  cathode  kept  cool 
by  water  does  not  lose  1/1500  of  what  it  should  lose,  if 
Faraday's  law  applied,  and  that  the  gain  on  the  anode  was 
very  slight. 

It  has  been  thought  by  some  that  disintegration,  such 
as  is  produced  by  boiling  or  by  oxidation,  must  occur  at 

1  Ann.  d.  Phys.,  37,  738;  1912. 

2  Paper  presented  at  Amer.  Electrochem.  Soc.,  in  1904. 


l8o  THE   ELECTRIC  ARC 

the  electrodes.  There  is  no  question  but  that  such  action 
at  the  cathode  makes  it  easier  for  the  current  to  flow, 
as  has  already  been  shown,  but  the  experiments  of  Weedon 
show  that  this  is  not  essential. 

There  has  been  some  discussion  as  to  whether  the  current 
is  carried  by  the  vapors  which  come  from  the  anode  or  by 
those  coming  from  the  cathode.  Steinmetz1  says  that  it  is 
carried  by  a  blast  from  the  cathode.  Blondel2  believes  that 
it  is  carried  by  material  coming  from  the  anode.  It  would 
seem  that  neither  of  these  views  is  entirely  correct.  The 
current  is  carried  by  that  part  of  the  vapor  between  the 
electrodes  which  is  the  most  conducting.  In  some  cases 
this  vapor  comes  largely  from  the  anode,  in  others  from 
the  cathode.  In  the  carbon  arc  where  the  anode  is  the 
hotter  the  anode  sends  more  conducting  vapor  into  the  arc 
than  the  cathode  does.  In  Steinmetz'  arc  between  a 
copper  anode  and  a  magnetite  cathode  the  copper  is  com- 
paratively cold  and  sends  no  vapor  into  the  arc,  while  the 
cathode  sends  into  it  vapor  that  is  highly  conducting. 

Variations  of  the  Cathode  Drop.  —  There  has  thus  been 
outlined  a  theory  of  the  arc  as  applied  to  the  simplest  form; 
namely,  the  arc  between  two  electrodes  which  are  alike, 
and  where  the  gas  of  the  arc  comes  from  the  electrodes. 
An  example  of  this  is  the  mercury  arc  in  which  both  elec- 
trodes are  mercury  and  the  gas  is  mercury  vapor.  But  this 
form  is  exceptional  in  its  simplicity.  With  the  majority  of 
arcs  there  is  a  combination  of  gases  to  be  considered  and 
a  chance  for  chemical  action  which  may  modify  to  a  large 
extent  the  electrical  conditions.  An  example  of  this  is  the 
open  carbon  arc  where  oxidation  continually  occurs. 

1  Trans.  Intern.  Elec.  Cong.,  St.  Louis,  2,  711;    1904. 

2  Trans.  Intern.  Elec.  Cong.,  St.  Louis^  2,  750;   1904. 


THEORY   OF   THE   ELECTRIC   ARC 

An  illustration  of  the  effect  produced  by  changing  some 
of  the  conditions  is  shown  when  different  metals  are  used 
for  the  cathode  of  an  arc  in  a  vacuum.  As  has  been  stated, 
it  is  difficult  to  maintain  such  an  arc  when  the  metal  used 
for  the  cathode  has  a  high  melting  point,  and  in  general  the 
higher  the  melting  point  of  the  cathode  metal,  the  greater 
the  cathode  drop  which  is  necessary.  The  difficulty  here 
is  not  altogether  due  to  the  heat  being  conducted  away 
from  the  hot  point  of  the  cathode,  for  the  thermal  conduc- 
tivity of  platinum  and  lead  are  nearly  the  same,  yet  lead 
can  easily  be  made  the  cathode,  while  platinum  can  not 
be  so  used  except  with  high  voltages.  The  thermal  con- 
ductivity of  zinc  is  greater  than  that  of  iron,  yet  zinc  may 
be  the  cathode  of  an  arc  in  a  vacuum,  while  iron  can  not. 

Whether  the  difficulty  is  due  to  the  hot  point  on  the 
cathode  being  too  cool  to  give  off  electrons  in  abundance, 
or  to  a  loading  of  these  ions  with  a  condensing  vapor  we 
can  not  at  present  say.  That  the  vapor  does  in  some  cases 
condense  on  the  negative  ions  is  known  to  be  a  fact  and  it 
may  well  be  the  cause  of  the  difficulty  here. 

Whatever  its  cause,  it  is  apparently  obviated  when  there 
is  a  chance  for  chemical  action  at  the  cathode.  Thus,  it  is 
easy  to  maintain  an  arc  with  the  oxide  of  a  metal  for  the 
cathode,  and  also  with  metals  in  air,  and  with  the  greater 
number  of  them  in  nitrogen.  There  is  no  great  difficulty  in 
maintaining  one  between  graphite  or  carbon  terminals  in 
hydrogen,  while  it  is  very  difficult  to  do  so  between  copper 
or  iron  terminals  in  that  gas. 

Apparently  it  is  easier  to  maintain  an  arc  when  there 
is  either  chemical  action  or  ebullition  at  the  cathode,  as 
if  ionization  could  occur  more  easily  when  physical  or  chem- 
ical change  is  occurring.  Even  with  carbon  in  hydrogen 


182  THE  ELECTRIC  ARC 

the  carbon  usually  loses  weight  as  if  some  chemical  or 
physical  change  were  taking  place. 

Again,  there  is  a  change  in  the  cathode  drop  when  the 
current  changes.  For  example  with  the  carbon  arc  in  air 
the  greater  the  current  flowing  the  less  the  cathode  drop. 
This  is  probably  due  to  the  increase  in  the  amount  of  heat 
developed  near  the  cathode.  Heat  at  this  point  will  do 
one  of  two  things.  It  will  either  raise  the  temperature  of 
the  cathode,  or  if  the  cathode  is  at  the  sublimation  point, 
it  will  increase  the  amount  of  vapor  sent  into  the  arc.  If 
the  cathode  becomes  hotter,  ionization  at  its  surface  will 
occur  with  less  vigorous  impact  and  a  smaller  cathode  drop 
will  be  sufficient  to  give  this  impact.  If  on  the  other  hand 
the  point  of  sublimation  has  been  reached,  and  more  vapor 
is  produced,  we  should  again  expect  a  smaller  cathode  drop 
for  we  have  already  seen  that  the  cathode  drop  is  least 
when  the  cathode  is  sending  vapor  into  the  arc,  as  it  does, 
for  example,  in  the  mercury  arc. 

It  is  indeed  more  difficult  to  explain  the  fact  that  the 
cathode  drop  of  the  mercury  arc  does  not  appear  to  change 
when  the  current  is  changed  (p.  96).  It  may  be,  how- 
ever, that  here  we  have  so  much  vaporization  at  all  times, 
that  a  limited  amount  more  or  less  does  not  produce  any 
appreciable  effect.  It  would,  however,  be  surprising  if  one 
should  find  that  the  cathode  drop  did  not  increase  some- 
what when  very  small  currents  were  used. 

The  pressure  of  the  surrounding  gas  also  affects  some- 
what the  value  of  the  cathode  drop,  the  drop  becoming 
larger  as  the  pressure  increases.  This  is  no  doubt  due  to 
the  more  rapid  dissipation  of  the  heat  caused  by  the  greater 
number  of  molecules  and  the  necessity  of  supplying  a  corre- 
spondingly greater  amount  of  heat  to  the  cathode.  It  may 


THEORY   OF   THE   ELECTRIC   ARC  183 

also  be  that  the  increase  in  the  number  of  molecules  impedes 
the  movement  of  the  ions  and  thus  makes  necessary  a 
greater  drop  in  potential. 

Variations  in  the  Anode  Drop.  —  So  long  as  the  anode  is 
kept  cool,  it  may  be  changed  without  producing  any 
appreciable  effect  in  the  anode  drop.  When  it  is  heated 
two  effects  may  occur.  The  first  of  these  was  pointed  out 
by  Stark,  Retschinsky  and  Schaposchnikoff1  who  called 
attention  to  the  fact  that  when  a  metal  becomes  very  hot 
it  tends  to  send  out  negative  ions,  and  if  the  metal  is  the 
anode,  these  ions  must  be  driven  back  again  into  the  metal. 
It  would,  therefore,  be  necessary  to  have  a  larger  anode 
drop  when  the  metal  is  hot  than  when  it  is  cool  (p.  97). 

In  the  second  place  the  conditions  become  quite  different 
when  the  anode  becomes  sufficiently  hot  to  vaporize.  This 
is  especially  true,  if  the  vapor  which  the  anode  sends  into 
the  arc  is  different  from  the  gas  existing  there  when  the 
anode  is  cool.  The  anode  drop  may  then  change  by  a 
very  appreciable  amount.  Such  a  change  no  doubt  occurs 
in  the  iron  arc  when  it  passes  from  the  first  to  the  second 
stage  (p.  65). 

The  anode  drop  is  also  very  greatly  affected  by  any  other 
change  in  the  kind  of  vapor  in  the  arc.  As  we  have  seen 
(p.  60),  the  introduction  of  a  salt,  such  as  sodium  carbonate, 
causes  the  anode  drop  to  be  very  much  lower.  Again,  if 
the  cathode  is  changed  so  that  a  different  vapor  comes  from 
it  into  the  arc,  the  anode  drop  is  changed.  Thus  I  found 
that  with  cored  carbon  for  both  anode  and  cathode  the 
anode  drop  was  38  volts.  With  the  same  current  and 
length  of  arc  and  the  same  anode,  but  with  iron  for  the 
cathode  the  anode  drop  was  14  volts.  Apparently  the 

1  Ann.  d.  Phys.,  18,  219;  1905. 


1 84  THE  ELECTRIC  ARC 

negative  ions  in  the  iron  vapor  do  not  require  so  large  a 
potential  difference  in  order  to  ionize  the  atoms  at  the 
surface  of  the  anode. 

The  anode  drop  in  the  carbon  arc  decreases  when  the 
current  increases.  As  was  the  case  with  the  cathode  drop 
this  may  be  due  to  an  increase  in  the  temperature  of  the 
anode  or  to  more  rapid  vaporization  of  the  carbon.  Those 
who  have  made  determinations  of  the  temperature  of  the 
anode  differ  as  to  whether  this  temperature  depends  on 
the  amount  of  current  flowing  or  not  (p.  45) ,  so  that  we  can 
not  tell  which  of  these  two  phenomena  should  be  expected 
to  follow  when  there  is  an  increase  in  the  current.  Either 
of  them  would  be  followed  by  a  lowering  of  the  anode  drop. 

The  cause  of  the  increase  of  the  anode  drop  when  the 
pressure  of  the  gas  is  increased  is  no  doubt  the  same  as 
the  corresponding  increase  in  the  cathode  drop.  The 
greater  the  pressure  the  faster  the  heat  is  taken  away  by 
molecules  of  the  gas  and  the  more  heat  must  be  produced 
by  the  current.  Again,  the  greater  the  number  of  mole- 
cules in  the  neighborhood  of  the  anode  the  more  the  ions 
passing  to  and  from  it  will  be  retarded. 

Variations  in  the  Electric  Force  through  the  Arc.  - 
The  electric  force  through  the  arc  is  changed  very  much 
when  the  kind  of  gas  is  changed,  as  when  a  salt  is  intro- 
duced into  the  arc  or  when  the  anode  becomes  sufficiently 
hot  to  send  vapor  into  the  arc.  This  force  also  depends  on 
the  kind  of  gas  in  which  the  arc  is  placed.  Thus  Stark, 
Retschinsky  and  Schaposchnikoff  found  that  the  electric 
force  between  either  copper  or  carbon  electrodes  was  greater 
when  the  carbons  were  in  hydrogen  than  when  they  were 
in  carbon  dioxide. 

The  cause  of  the  change  in  some  cases  is  the  greater  ease 


THEORY  OF  THE  ELECTRIC  ARC  185 

with  which  some  substances  are  ionized  than  other  sub- 
stances. Thus  sodium  carbonate,  when  at  a  high  tem- 
perature, appears  to  be  much  more  easily  ionized  than  air. 
In  other  cases  the  change  may  be  due  to  the  greater  rapidity 
with  which  heat  is  conducted  away  by  the  gas  as  with  an 
arc  placed  in  hydrogen.  It  is  probable  that  a  large  part 
of  the  decrease  in  the  potential  difference  between  the 
terminals  of  an  iron  arc  when  it  passes  from  the  first  to  the 
second  stage  is  due  to  the  greater  ease  with  which  the  gas 
from  the  vaporizing  metal  anode  can  be  ionized. 

Effect  Produced  by  Heating  the  Cathode.  —  To  produce 
the  high  temperature  of  the  cathode  there  must  be  an 
expenditure  of  electrical  energy  in  its  neighborhood.  The 
rate  at  which  this  is  done  equals  the  cathode  drop  times 
the  current.  It  is  natural  to  expect  that  if  the  cathode  is 
cooled  artificially,  it  will  require  a  greater  expenditure  of 
energy  to  maintain  the  needed  temperature,  and  to  do  this 
with  a  given  current  the  cathode  drop  must  be  greater. 
Similarly,  with  any  method  of  heating  we  should  expect 
the  cathode  drop  to  be  less. 

But  it  was  found  (p.  48)  that  cooling  the  cathode  pro- 
duced but  a  slight  effect  on  the  cathode  drop,  while  it  had 
a  very  appreciable  effect  on  the  anode  drop  and  on  the 
fall  of  potential  through  the  arc.  A  possible  explanation  for 
this  is  that  it  is  a  mistake  to  suppose  that  the  temperature 
of  the  cathode  must  be  kept  at  a  certain  definite  value.  It 
is  probable  that  there  may  be  conditions  where  this  tem- 
perature is  lower  than  that  which  is  commonly  found.  How- 
ever, when  the  temperature  of  the  cathode  is  lowered,  it 
sends  out  fewer  electrons  and  as  a  result  the  remaining  parts 
of  the  arc  have  a  smaller  conductivity,  so  that  we  get  the 
effects  which  have  been  observed. 


INDEX 

(The  numbers  refer  to  pages.) 


Abey  and  Festing,  43. 
Alternating-current  arc: 

with  carbon  electrodes,  105. 

characteristic  curves  for,  106. 

current  and  potential   difference 
for  different  phases  of,  107. 

oscillographs  for,  109. 

dynamical    characteristic    curves 
for,  no. 

anode  and  cathode  drops  in,  112. 

phase  difference  in,  113. 

between  metals,  114. 

in  a  vacuum,  117. 

between  unlike  terminals,  118. 

in  other  gases  than  air,  119. 

candle  power  of,  135. 

photometry  of,  135. 
Amalgams,  arc  between,  102. 
Andrews,  48. 
Anode: 

definition  of,  4. 

temperature  of,  40,  165. 

ionization  at,  162,  168. 

effect  produced  by  heating,  185. 

See  also  Electrodes  and  Crater. 
Anode  drop: 

definition  of,  22. 

in  carbon  arc  in  air,  24. 

in  flaming  arc,  60. 

with  copper  electrodes,  65. 

with  graphite  electrodes,  66. 

with  metal  electrodes,  66. 

with  unlike  electrodes,  72. 


Anode  drop: 

in  a  vacuum,  78. 

in  mercury  arc,  97. 

in  alternating-current  arc,  112. 

theory  of,  168. 

variations  in,  183. 
Appearance  of  arc: 

carbon  arc  in  air,  3. 

flaming  arc,  54. 

magnetite  arc,  67. 

arc  in  a  vacuum,  75. 

mercury  arc,  88. 

alternating-current  arc,  105. 
Arnold,  Cody  and,  64,  145. 
Arons,  30,  37,  71,  82,  87,  92,  96,  103, 

114,  116,  164. 
Austin,  153. 
Ayrton,  31,  131. 
Ayrton,  Mrs.,  10,  21,  24,  48,  130. 

B 
Back  E.M.F.,  see  Counter  E.M.F. 

Baeyer,  Gehrke  and,  103. 

Baldwin,  Miss,  143. 

Banderet,  66. 

Becknell,  38. 

Becquerel,  41. 

Bedell,  124. 

Blondel,  16,  37,  50,  119,  130,  132, 

139,  170,  180. 

Blondel  lamp,  candle  power  of,  139. 
Boston  flaming  arc,  candle  power  of, 

140. 
Braun,  147. 


187 


i88 


INDEX 


Bremen,  56. 

Bremen  lamp,  candle  power  of,  139. 

Brilliancy  of  crater,  132. 

Bron,  Guye  and,  115. 

Burgess,  Waidner  and,  43,  173. 


Cody  and  Arnold,  64,  145. 

Cody  and  Vinal,  65. 

Calcium  fluoride  in  flaming  arc,  56. 

Calcium  oxide  at  cathode,  82. 

Candle  power: 

of  direct-current  carbon  arc,  128. 

and  area  of  crater  visible,  129. 

as  affected  by  length  of  arc,  cur- 
rent, etc.,  130. 

of  flaming  arcs,  133. 

of  mercury  arc,  134. 

of  alternating-current  arcs,  135. 

comparison  of,  139. 
Carbon  arc  in  air: 

characteristic  curves  for,  9. 

E.M.F.  required,  16. 

potential  in  different  parts  of,  22. 

cathode  drop  in,  22. 

anode  drop  in,  24. 

electric  force  in,  24. 

counter  E.M.F.  of,  25. 

temperature  of,  40. 

with  alternating  currents,  105. 

candle  power  of,  128. 
Carbon  arc  in  vacuum: 

appearance  of,  75. 

voltage  with  different  pressures,  78. 

anode  and  cathode  drops  in,  78. 

voltage  with  different  lengths,  79. 

temperature  of,  81. 

with  alternating  currents,  117. 
Carbon  electrodes: 

manufacture  of,  8. 


Carbon  electrodes: 

solid,  8. 

cored,  9. 

diameter  of,  and  candle  power, 

137. 

Carbon  dioxide,  arc  in,  85. 
Carbon  monoxide,  arc  in,  85. 
Carbone  lamp,  133. 
Casselmann,  55. 
Cassuto,  Stark  and,  163. 
Cathode: 

definition  of,  4. 

area  of,  49. 

ionization  at,  161,  165. 

must  be  hot,  162. 

temperature  of,  165. 

effect  produced  by  heating,  185. 
Cathode  drop: 

definition  of,  22. 

in  carbon  arc  in  air,  22. 

in  flaming  arc,  60. 

with  copper  electrodes,  65. 

with  graphite  electrodes,  66. 

with  unlike  electrodes,  72. 

in  a  vacuum,  78. 

in  mercury  arc,  96. 

in  alternating  arc,  112. 

theory  of,  166. 

variations  in,  180. 
Characteristic  curves: 

definition  of,  12. 

for  arcs  between  solid  carbons,  13. 

for  arcs  between  cored  carbons,  14. 

statical,  16. 

dynamical,  16,  no,  151. 

for  enclosed  arc,  50. 

for  flaming  arc,  58. 

for  arc  between  metals,  62. 

for  magnetite  arc,  67. 

for  iron-titanium  arc,  69. 

for  mercury  arc,  93. 


INDEX 


Characteristic  curves: 

for  alternating-current  arc,  106,  no. 
Cheneveau,  51. 
Color  of: 

flaming  arc,  54. 

mercury  arc,  88. 

carbon  arc,  126,  142. 
Conductivity  of  arc,  see  Resistance. 
Consumption  of  electrodes,  49,  139. 
Cooling  of  electrodes,  46,  185. 
Cooper  Hewitt,  87,  95,  103,  120. 
Cooper  Hewitt  mercury  vapor  lamp, 

89. 

Copper  electrodes,  arc  between,  62. 
Corbino  and  Liga,  37. 
Cored  carbons: 

manufacture  of,  9. 

characteristic  curves  for,  14. 

anode  drop  with,  24. 

cathode  drop  with,  24. 
Cores,  composition  of,  9. 
Counter  E.M.F.  of  arc,  10,  25. 
Crater: 

definition  of,  4. 

temperature  of,  40. 

area  of,  and  current,  48. 

area  of,  and  candle  power,  129. 

intrinsic  brightness  of,  132. 
Cunningham,  165. 
Current: 

and  potential  difference,  see  Char- 
acteristic curves. 

oscillation  of,  with  hissing  arc,  21. 

with  different  phases  of  alternat- 
ing-current arc,  107. 

rectifier,  120. 

and  candle  power,  130. 

D 

Davis,  159,  173. 
Davy,  6,  50,  62,  74. 


Definition  of: 

arc,  i. 

anode,  4. 

cathode,  4. 

characteristic  curves,  12. 

ions,  156. 

electrons,  156. 
De  la  Rive,  46,  74. 
De  la  Rue  and  Mutter,  74. 
Dewar,  41,  51. 
Discharge  in  vacuum  compared  with 

arc,  2. 
Discovery  of: 

carbon  arc,  5. 

mercury  arc,  88. 
Distribution  of  light  with: 

direct-current  carbon  arc,  128. 

alternating-current     carbon     arc, 

136. 

Dubs,  38. 
Duddell,  15,  28,  32,  116,  136,  148, 

152. 

Duddell  and  Mar  chant,  22,  112. 
Duncan,  Rowland  and  Todd,  73. 
Dynamical  characteristic  curves,  16, 

no,  151. 
Dyott,  68. 


Edlund,  9,  25,  35,  62. 

Efficiency  of  arc,  see  Candle  power. 

Electric  force  in  arc: 

in  air,  24. 

in  vacuum,  78. 

mercury  arc,  97. 

theory  of,  173. 

variations  of,  184. 
Electrodes: 

arc  between  carbon,  8. 

manufacture  of,  8,  56. 

consumption  of,  49,  139. 


INDEX 


Electrodes : 

light  from,  129. 

discharge  of  ions  to,  170. 

Ste  also  Metal  electrodes,  Oxides, 
Magnetite,  Electrolyte,  and  Un- 
like. 
Electrolytes: 

arc  between,  69. 

arc  not  like,  179. 
Electrons: 

definition  of,  156. 

coming  from  within  metal,  163. 
E.M.F.: 

counter,  10,  25. 

required  for  arc,  16 

"  forward,"  33. 

residual,  35. 
Enclosed  arc: 

description  of,  49. 

characteristic  curves  for,  50. 

candle  power  of,  137,  139. 
Exploring  electrodes,  22. 


Feige,  Urbain,  Seal  and,  103. 

Fery,  43,  93. 

Festing,  Abey  and,  43. 

Firth,  31. 

Firth  and  Rogers,  22,  32. 

Fitzgerald,  Wilson  and,  45,  73. 

Flaming  arc: 

appearance  of,  54. 

history  of,  55. 

composition  of  electrodes  with,  56. 

advantages  of,  57. 

characteristic  curves  for,  58. 

anode  and  cathode  drops  in,  60. 

with  alternating  currents,  109. 

photometry  of,  132. 

candle  power  of,  133. 
Fleming,  23. 


Fleming  and  Petavel,  127,  137. 
Foley,  143. 

"  Forward,"  E.M.F.,  33, 
Freedman,  63. 


Gas  between  electrodes: 

temperature  of,  40. 

ionization  of,  171. 
Gases,  arc  in  various,  83,  119. 
Gehrke  and  Baeyer,  103. 
General  Electric  Company: 

mercury  vapor  lamp,  90. 

mercury  arc  rectifier,  122. 
Georges,  136. 
Glow  discharge,  2. 
Gould,  118. 
Granqvist,  37,  49,  JI4- 
Grau  and  Russ,  63,  85. 
Gray,  Wilson  and,  41. 
Grove,  69. 

Guye  and  Bron,  115. 
Guye  and  Monash,  115. 
Guye  and  Zebrikojf,  63. 

H 

Hagenbach  and  Veillon,  64. 

Hall  effect  in  mercury  arc,  102,  178. 

Heinke,  34. 

Hertzfeld,  137. 

Heubach,  106,  113. 

Hewitt,  see  Cooper  Hewitt. 

Hissing  arc: 

voltage  of,  21. 

cause  for,  21. 

with  metals,  65. 
History  of  arc,  5. 
Hittorf,  165. 
Hoerburger,  79. 
Horton,  160. 
Hotchkiss,  38. 


INDEX 


Evil,  144. 
Humphreys,  145. 
Hydrogen,  arc  in, 


Intrinsic  brightness  of  crater,  132. 
lonization: 

by  impact,  158. 

by  hot  solids,  159. 

at  surface  of  cathode,  161,  162, 
165- 

at  surface  of  anode,  162,  168. 

of  gas  between  electrodes,  171. 

by  ultra-violet  light,  172. 
Ions: 

velocity  of,  101,  176. 

definition  of,  156. 

causes  producing,  158. 

discharge  of,  to  electrodes,  170. 
Iron  electrodes,  64. 
Iron-titanium  arc: 

characteristic  curves  for,  69. 

candle  power  of,  139. 

J 

Jamin  and  Maneuvier,  114,  118. 
Janet,  152. 
Joubert,  107. 


Kayser,  144. 

Knipp,  92,  96,  97. 

Kuch  and  Retschinski,  100,  135. 

Kuch,  Stark  and,  81. 


Lamp,  mercury  vapor,  89. 
Lange,  Gertrude,  112. 
Le  Chatelier,  41. 
Lecher,  24,  37,  46,  63,  66. 
Lenard,  144. 


Length  of  arc: 

and  candle  power,  130. 

and  potential  difference,  see  Char- 
acteristic curves. 
Le  Roux,  37,  106. 
Liga,  Corbino  and,  37. 
Light  from  arc: 

quality  of,  see  Color. 

quantity  of,  see  Candle  power. 
Luggin,  24,  28,  31,  37,  60,  163. 
Luminous  vapor  from  mercury  arc, 

99. 
Lummer  and  Pringsheim,  43. 

M 

McClelland,  177. 
Magnetic  field: 

carbon  arc  in,  6,  50. 

whistling  arc  in,  151. 
Magnetite  arc: 

characteristic  curves  for,  67. 

candle  power  of,  139,  140. 

ionization  in,  180. 
Mahlke,  9,  56. 

Malcolm  and  Simon,  15,  48,  64,  83. 
Maneuvier,  Jamin  and,  114,  118. 
Manufacture  of  carbons,  8. 
Mar  chant,  133. 

Marchant,  Duddell  and,  22,  112. 
Marks,  49. 
Matthies,  179. 
Matthews,  137. 

Mean  free  path  of  ions  in  arc,  173. 
Mean  spherical  candle  power,  128. 
Mercury  arc: 

discovery  of,  88. 

commercial  form  of,  89. 

temperature  of,  91. 

characteristic  curves  for,  93. 

pressure  in,  94. 

cathode  drop  in,  96. 


IQ2 


INDEX 


Mercury  arc: 

anode  drop  in,  97. 

electric  force  in,  97. 

in  quartz  tubes,  100. 

velocity  of  ions  in,  101. 

modification  of,  to  produce  white 
light,  102. 

rectifier,  120. 

with  alternating  currents,  124. 

photometry  of,  134. 

candle  power  of,  134,  139,  142. 
Merritt  and  Stewart,  177. 
Metal  electrodes: 

arc  with,  61. 

characteristic  curves  with,  62. 

hissing  arcs  with,  65. 

anode  and  cathode  drops  with,  65. 

different  metals  used  for,  66,  81, 

115- 

in  a  vacuum,  81. 

with  alternating  currents,  114. 

photometry  of;  134. 
Metteucci,  62. 
Microphone  and  wireless  telephony, 

154- 

Milkiewicz,  38. 
Moissan,  40. 
Monash,  Guye  and,  115. 
Morris,  51,  120. 
Miiller,  de  la  Rue  and,  74. 

N 

Negative  electrode,  see  Cathode. 
Negative  ions,  157. 
Negative  resistance,  31. 
Nitrogen  arc  in,  84. 
Non-arcing  metals,  114. 
Norden,  124. 

O 

Olivette,  38. 
Oscillograph,  38. 


Oscillographs  of: 

hissing  arc,  21. 

arc  in  magnetic  field,  51. 

alternating-current  arc,  109. 
Oxides,  arc  between,  67. 
Oxygen,  arc  in,  85. 


Petavel,  41,  132. 
Petavel,  Fleming  and,  127,  137. 
Phase    difference    between    current 
and    voltage  with  alternating- 
current  arcs,  113. 
Photometry: 

difficulties  in,  126. 

of  direct-current  carbon  arc,  128. 

of  flaming  arc,  132. 

of  metal  arcs,  134. 

of  mercury  arc,  134. 

of  alternating-current  arc,  135. 

See  also  Candle  power. 
Planck's  law,  43. 
Pollak,  96,  98,  175. 
Pollock,  34. 

Pollock  and  Ranchaud,  52. 
Positive  electrode,  see  Anode. 
Positive  ions,  157. 
Potassium  alloy,  82. 
Potential    difference    between    ter- 
minals of: 

carbon  arc,  9. 

arc  in  vacuum,  78,  79. 

arc  in  hydrogen,  86. 

See  also  Characteristic  curves. 
Potential   difference   with   different 
phases    of    alternating-current 
arc,  107. 

Potential  gradient,  see  Electric  force. 
Potential  within  arc,  22,  160. 
Poulsen,  151. 
Power  used  in  arc,  14. 


INDEX 


Pressure  in  mercury  arc,  94. 
Pressures  greater  than  one  atmos- 
phere, 73. 

Pringsheim,  Lummer  and,  43. 
Puccianti,  144." 
Pyrometer,  44. 


Quartz  tubes  for  mercury  arc,  100. 


Ranchaud,  Pollock  and,  52. 

Rasch,  67. 

Rectifier,  mercury  arc: 

three-phase,  120. 

single-phase,  122. 
Reich,  45,  49,  165. 
Residual  E.M.F.,  35. 
Resistance : 

of  arc,  9,  28. 

in  series  with  arc,  22. 

negative,  31. 

after  removal  of  E.M.F.,  38. 
Retschinski,  Kuch  and,  100,  135. 
Retschinski,  Stark  and  Schaposchni- 

ko/,  83,  96,  97,  168,  178,  183. 
Rey,  132. 

Richardson,  O.  W.,  159,  164. 
Rogers,  Firth  and,  22,  32. 
Rosetti,  41. 

Rossler  and  Wedding,  137. 
Rowland,  Duncan  and  Todd,  73. 
Ruhmer,  148. 
Russ,  Grau  and,  63,  85. 
Ryan,  140. 


Sahulka,  69,  118. 

Salts,  effect  of,  in  arc,  55. 

Seal,  Urbain,  and  Feige,  103. 


Schaposchniko/,    Stark,   Retschinski 
and,  83,  96,  97,  169,  178,  183. 

Schenkel,  101,  178. 

Schultze,  48,  67. 

Sharpe,  133. 

Silent  arc,  21. 

Simon,  16,  109,  146,  151. 

Simon,  Malcolm  and,  15,  48,  64,  83. 

Skinner,  168. 

Sodium  alloy  for  electrodes,  82. 

Solid  carbons,  9. 
characteristic  curves  with,  13. 

Spark  compared  with  arc,  2. 

Spectrum  of  carbon  arc,  142. 

Stability  of  arc,  conditions  for,  18. 

Stark,  82,  99,  156,  164. 

Stark  and  Cassuto,  163. 

Stark  and  Kuch,  81. 

Stark,  Retschinski  and  Schaposchni- 
koff,  83,  96,  97,  168,  178,  183. 

Static  converter,  120. 

Statical  characteristic  curves,  16. 

Stefan-Boltzmann  law,  42. 

Steinmetz,  114,  145,  180. 

Stenger,  37,  74. 

Stewart,  Merritt  and,  177. 

Sulphur  dioxide,  arc  in,  85. 

Swendler,  29. 

Swinton,  177. 


Telephony,  wireless,  and  arc,  146. 
Temperature  of: 

gas  in  carbon  arc,  40. 

anode  of  carbon  arc,  40. 

variation  of,  44. 

arc  in  vacuum,  81. 

mercury  arc,  91. 
Terminals,  see  Electrodes. 
Theory  of  arc,  156. 


194 


INDEX 


Thomson,  E.,  148. 

Thomson,  Sir  J.  J.,  156,  170,  176. 

Titanium  arc,  68. 

Tobey  and  Walbridge,  107. 

Todd,  Duncan,  Rowland  and,  73. 

Tommasi,  48. 

Townsend,  158,  173. 

Trotter,  51,  129. 


U 

Ultra-violet  light: 
produced  by  arc,  100. 
ionization  by,  172. 

Unlike  electrodes,  69,  118. 

Uppenborn,  24. 

Upson,  63. 

Urbain,  Seal  and  Feige,  103. 


Vacuum,  arc  in,  74,  81,  117. 

Van  Breda,  74. 

Variation    in    temperature   of    arc, 

44. 

Veillon,  Hagenbach  and,  64. 
Velocity  of  ions  in: 

mercury  arc,  101. 

carbon  arc,  177. 
Very,  43. 

Vinal,  Cody  and,  65. 
Violle,  42. 


Voltage  of  arcs,  see  Potential  differ- 
ence between  terminals. 
Von  Lang,  29,  63. 

W 

Waidner  and  Burgess,  43,  173. 

Walbridge,  Tobey  and,  107. 

Walker,  50. 

Wanner,  43. 

Wave  form  and  candle  power,  137. 

Wedding,  133. 

Wedding,  Rossler  and,  137. 

Weedon,  69,  85,  179. 

Wehnelt,  159. 

Weintraub,  82,  122. 

Wey,  88. 

Whispering  arc,  146. 

Whistling  arc,  148. 

Wien's  law,  42. 

Wild,  36. 

Wilde,  ST.. 

Wills,  92. 

Wilson  and  Gray,  41. 

Wilson  and  Fitzgerald,  45,  73. 

Wilson,  H.  A.,  160. 

Wilson,  W.  E.,  45,  132. 

Wireless  telephony,  use  of  arc  in, 

146. 

Wood's  metal,  arc  with,  82. 
Wurts,  114. 


Zebrikof,  Guye  and,  63. 


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THOMPSON,  S.  P.  Dynamo-Electric  Machinery.  With  an  Introduction 
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URQUHART,  J.  W.  Electroplating.  A  Practical  Handbook.  Fifth 
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WEEKS,  R.  W.      The  Design   of  Alternate-Current  Transformer. 

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WEYMOUTH,  F.  MARTEN.  Drum  Armatures  and  Commutators. 
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WILKINSON,  H.  D.  Submarine  Cable  Laying,  Repairing  and  Testing. 
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WRIGHT,  J.  Testing,  Fault  Localization  and  General  Hints  for  Linemen. 
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ZEIDLER,  J.,  and  LUSTGARTEN,  J.  Electric  Arc  Lamps:  Their  Princi- 
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